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

Given, S(m) -S(n) = 0

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

Or (m-n)a + [(m² -m) - (n² -n)]d/2 = 0

Or (m-n)a + (m-n)[m + n -1]d/2 = 0

Or (m-n)[2a + (m+n-1)d] = 0 —— (multiplying both sides of eqn by 2)

Or (m-n) x S(m+n) = 0

Which means either (m-n) = 0 or S(m +n) = 0.

Hence, S(m+n) = 0

Amannnscharlie

Answer 2

Answer:

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