Question
Thu September 03, 2009 By: Khushal Gupta

A.P.

Expert Reply
Thu September 03, 2009

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

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

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

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

(1) - (2) gives,

(m-1)d - (n-1)d  = 2n/m - 2m/n

(m-n)d = 2(n2-m2)/mn

d = -2(m+n)/mn

Sm+n = (m+n)(2a+(m+n-1)d)/2 

 = m(a+(m+n-1)d)/2 + n(a+(m+n-1)d)/2

= n + mnd/2 + m + mnd/2

= n + mnd + m

= (m+n) + mn(-2(m+n)/mn)           ............................substituting the value d.

= -(m+n)

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Team,

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