Let denote the sum of the first odd natural numbers.

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Play · Number Play

Problem

Let

S_n

denote the sum of the first

n

odd natural numbers. (i) Express

S_n

using summation notation. (ii) Prove that

S_n=n^{2}

. (iii) Hence evaluate

\displaystyle \sum_{k=51}^{100}(2k-1)

without direct addition of terms.