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mathematics
precalculus

Questions and Answers of Precalculus

Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 2 – 1 + 4
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 2 + 1 + 4
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 3 + 1 + - 3
Find a general formula for the arithmetic sequence. 12th term is 30; 22nd term is 50
Find a general formula for the arithmetic sequence. 10th term is 0; 18th term is 8
Find a general formula for the arithmetic sequence. 8th term is 17th term is -20; -47
Find a general formula for the arithmetic sequence. 7th term is 31; 20th term is 96
Find the indicated term in the sequence. 9th term of √2, 2, 23/2 …
Find the indicated term in the sequence. Find the indicated term in the sequence. 9th term of √2, 2√2, 3√2 …
Find the indicated term in the sequence.11th term of 1, 2, 4, 8, ...
Find the indicated term in the sequence. 11th term of 1, 10' 100
Find the indicated term in the sequence.8th term of 1, -1, -3, -5, ...
Find the indicated term in the sequence.9th term of 3, 7, 11, 15, ...
Find the sum. 10 Σ-2) k k=1
Find the sum. k 3 k=1
Find the sum. 40 Σ(-2k + 8 ) k=1
Find the sum. 30 Σ (3k-9) k=1
Find the sum. 30 Σ2 k=1
Find the sum. 50 Σ (3k) k=1
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Express each sum using summation notation. 22 2 + 23 2"+1 3" 3 32 2.
Express each sum using summation notation. + · . ·+ 4 13
Write out the sum. 3 Σ (3-) 2. k=1
Write out the sum. E (4k + 2) k=1
Write down the first five terms of each sequence.a1 = -3; an = 4 – an-1
Write down the first five terms of each sequence.a1 = 2; an = 2 – an-1
Write down the first five terms of each sequence. An-1 ат — 4; ат ||
Write down the first five terms of each sequence. a1 = 3; an An-1 3 an
Write down the first five terms of each sequence. {d,} п
Write down the first five terms of each sequence.
Write down the first five terms of each sequence.{bn} = {(-1)n+1(2n + 3)}
Write down the first five terms of each sequence. - {-»} n + 3 {(-»( {a,} n + 2
Find the next term. + 4 4 3 3 3 : ?
An approximation for n!, when n is large, is given by Calculate 12!, 20!, and 25! on your calculator. Then use Stirling’s formula to approximate 12!, 20!, and 25!. п n! - V2n7| 12n – 1
If n is a positive integer, show that
If n is a positive integer, show that
Show that if n and j are integers 0 ≤ j ≤ n with thenConclude that the Pascal triangle is symmetric with respect to a vertical line drawn from the topmost entry (;) - (,-) п
Show that = n and 1. - 1 -('",")
Use the Binomial Theorem to find the numerical value of (0.998)6 correct to five decimal places
Use the Binomial Theorem to find the numerical value of (1.001)5 correct to five decimal places.
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x2 in the expansion of 3 Vx + Vx,
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x4 in the expansion of 10 Vx,
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x0 in the expansion of
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x0 in the expansion of 12 x² + х.
Use the Binomial Theorem to find the indicated coefficient or term. The sixth term in the expansion of (3x + 2)8
Use the Binomial Theorem to find the indicated coefficient or term. The third term in the expansion of (3x – 2)9
Use the Binomial Theorem to find the indicated coefficient or term. The third term in the expansion of (x – 3)7
Use the Binomial Theorem to find the indicated coefficient or term. The fifth term in the expansion of (x + 3)7
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x2 in the expansion of (2x – 3)9
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x7 in the expansion of (2x + 3)9
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x3 in the expansion of (2x + 1) 12
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x7 in the expansion of (2x – 1)12
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x3 in the expansion of (x – 3)10
Use the Binomial Theorem to find the indicated coefficient or term. The coefficient x6 in the expansion of (x + 3)10
Expand the expression using the Binomial Theorem. (ax + by)4
Expand the expression using the Binomial Theorem. (ax + by)5
Expand the expression using the Binomial Theorem. (√x + √3)4
Expand the expression using the Binomial Theorem. (√x + √2)6
Expand the expression using the Binomial Theorem. (x2 - y2)6
Expand the expression using the Binomial Theorem. (x2 + y2)5
Expand the expression using the Binomial Theorem. (2x + 3)5
Expand the expression using the Binomial Theorem.(3x + 1)4
Expand the expression using the Binomial Theorem. (x + 3)5
Expand the expression using the Binomial Theorem. (x - 2)6
Expand the expression using the Binomial Theorem. (x - 1)5
Expand the expression using the Binomial Theorem. (x + 1)5
Evaluate the expression. 37 19
Evaluate the expression. 47 25
Evaluate the expression. 60 20
Evaluate the expression. 55 23
Evaluate the expression. 1000
Evaluate the expression. 1000 1000
Evaluate the expression. 100 98
Evaluate the expression. 50 49
Evaluate the expression. 6, 7)
Evaluate the expression. 5
Evaluate the expression.
Evaluate the expression. (3.
The __________ can be used to expand expressions like (2x + 3)6.
True or False. j! (п — ј)! n! п
________ is a triangular display of the binomial coefficients.
For the sequence given in Problem 97, show thatun+1 + un = (n +1)2
For the sequence given in Problem 97, show that Data from Problem 97u1 = 1, un +1 = un + (n + 1). (n + 1)(n + 2) Un+1 2
A triangular number is a term of the sequence u1 = 1, un +1 = un + (n + 1). Write down the first seven triangular numbers.
A method for approximating √p can be traced back to the Babylonians. The formula is given by the recursively defined sequencewhere k is an initial guess as to the value of the square root. Use this
A method for approximating √p can be traced back to the Babylonians. The formula is given by the recursively defined sequencewhere k is an initial guess as to the value of the square root. Use this
A method for approximating √p can be traced back to the Babylonians. The formula is given by the recursively defined sequencewhere k is an initial guess as to the value of the square root. Use this
A method for approximating √p can be traced back to the Babylonians. The formula is given by the recursively defined sequencewhere k is an initial guess as to the value of the square root. Use this
Show that LetS = 1 + 2 + ... + (n - 1) + n S = n + (n - 1) + (n - 2) + ... + 1 Add these equations. Then Now, complete the derivation. п(п + 1) |1 + 2 +... + (n — 1) + п %3

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