If sum of first m terms of Ap is
the same as the sum of its
n terms show that the sum of its
first (m+n) terms is zero
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Answer:
m(a+(m-1)d)=n(a+(n-1)d)
ma+m(m-1)d=na+n(n-1)d
ma-na=n(n-1)d-m(m-1)d
a(m-n)=d(n^2-n-m^2+m)
a(m-n)=(n^2-m^2-(n-m)d)
a(m-n)=((n-m)(n+m)-(n-m)d)
a(m-n)=n-m(n+m-1)d
divide by m-n on both the sides
a= -1(n+m-1)d
a+(n+m-1)d=0
a m+n =0
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