The sum of first n odd natural numbers is

Question:

The sum of first n odd natural numbers is

(a) 2n +

(b) n2  

(c) n2 –1   

(d) n2 +1

Solution:

(b) Sum of first $n$ odd natural numbers $=\Sigma(2 n-1)=2 \Sigma n-n$

$=\frac{2 \times n(n+1)}{2}-n=n(n+1)-n=n^{2}+n-n=n^{2}$

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