Question

If the sum of m terms of an A.P. is n and sum of n terms is m, then show that the sum of its first (m+n) terms is -(m+n).

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

QED

Step-by-step explanation:

let a is 1st term and d is difference of AP

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

2am +m^2d - md = 2n     Eq A

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

2an + n^2d - nd = 2m    Eq B

EqA - Eq B

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

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

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

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

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

= - (m+n)

QED