Question

If the sum of first m terms of an AP is
the same as the sum of its first n terms, show
that the sum of its first (m+n) terms is zero​

Answer 1

Answer: Sm+n = 0. Proof.

Step-by-step explanation:

Sm = Sn

m/2 *( 2a + (n-1)d) = n/2 * (2a +(n-1)d)

m(2a) + m(n-1)d = n(2a) + n(n-1)d) =0

2a(m-n) + d(m^2 - m -n^2 +n) =0

2a(m-n) + d(m^2 -n^2 - m+n) =0

(m-n) (2a + (m+n-1)d) =0

Sm+n = (m+n)/2 * (2a + (m+n-1)d)

            (m+n)/2 * 0

          = 0

Answer 2

Step-by-step explanation:

here is your answer and once try to solve it yourself