(a) Compute the following sums of consecutive positive odd integers. (b) Use the sums in part (a)...

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(a) Compute the following sums of consecutive positive odd integers.
1 + 3 = 1 + 3 + 5 = 1 + 3 + 5 + 7 = 1 + 3 + 5 + 7 + 9 = 1 + 3 + 5 + 7 + 9 + 11 =

(b) Use the sums in part (a) to make a conjecture about the sums of consecutive positive odd integers. Check your conjecture for the sum

1 + 3 + 5 + 7 + 9 + 11 + 13 =

(c) Verify your conjecture algebraically.

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