Question

If n is odd, then (1+3+5+7......n terms) is equal to

Answer 1

Answer:

Answer n will bee equal to n^2 as it is a series Here

a=1 d=2 Sn=n/2 (2 (1)+(n-1)2)

sn=n/2 (2+2n-2)

sn=n/2 (2n)

sn=n^2

hope it'll help you!!!

Answer 2

Answer:

The sum of first n odd terms will be equal to n².

Step-by-step explanation:

For  the given series (1+3+5+7+........n)

First term, $a=1$  and common difference, $d=3-1=2$

We know that for arithmetic progression, sum is given by:

           $S_{n}=\frac{n}{2}(2a+(n-1)d)$

Fill the values of a and d in above equation:

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

 ⇒      $S_{n}=\frac{n}{2} (2+2n-2)$

 ⇒      $S_{n}=\frac{n}{2}(2n)$

 ∴        $S_{n}=n^{2}$