Question

how to show that sum of n odd terms =n^2​ correct answers please
quick
quick
quick​

Answer 1

Answer:

Explanation:

Let S(n) = 1 + 3 + 5 + · · · + (2n − 1). We want to prove

by induction that for every positive integer n, S(n) = n2.

1. Basis Step: If n = 1 we have S(1) = 1 = 12, so the property is

true for 1.

2. Inductive Step: Assume (Induction Hypothesis) that the property is true for some positive integer n, i.e.: S(n) = n2. We must

prove that it is also true for n + 1, i.e., S(n + 1) = (n + 1)2. In

fact:

S(n + 1) = 1 + 3 + 5 + · · · + (2n + 1) = S(n) + 2n + 1 .

But by induction hypothesis, S(n) = n2, hence:

S(n + 1) = n2 + 2n + 1 = (n + 1)2