Question
Let S(n) = 1 + 2 +???..+ n be the sum of the first n natural numbers and let C(n) =13 + 23 + -
Let S(n) = 1 + 2 +???..+ n be the sum of the first n natural numbers and let C(n) =13 + 23 + - + n3 be the sum of the first n cubes. Prove the following equalities by induction on n, to arrive at the curious conclusion that C(n) = S 2 (n) for every n.
a.
b.
S(n) = n(n+1). C(n) = (n + 2n + n) = n(n + 1)
Step by Step Solution
3.32 Rating (158 Votes )
There are 3 Steps involved in it
Step: 1
a The sum of the first n natural numbers S n 1 2 3 n is given by Hence induction method is us...
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started
A Survey of Mathematics with Applications
Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde
10th edition
134112105, 134112342, 9780134112343, 9780134112268, 134112261, 978-0134112107
