CBSE sample paper questions ....please solve this ques
1. If the sum of first m terms of AP is n and the sum of first n terms is m then show that the sum of first m+n terms is -(m+n).
1. If the sum of first m terms of AP is n and the sum of first n terms is m then show that the sum of first m+n terms is -(m+n).
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LET a Be The First Term And d Be c.d. Of The A P .
THEN,
Sm=n
n= m/2{2a+ (m-1)d}
2n= 2am+ m( m-1)d. ........(1)
and
Sn= m
m= n/2{2a+(n-1)d}
2m= 2an+ n(n-1)d. ...........(2)
Subtracting eq.(2)- (1),
we get
2a(m-1)+{m(m-1)- n(n-1)}d =
2n-2m
2a(m-n) +{(m^2-n^2)-(m-n)}
d = -2(m-n)
2a +(m+n-1) d = -2.
[On dividing both sides by
( m-n)]………(3)
Now,
Sm+n=m+n/2{2a +(m+n-1)d}
Sm+n=m+n/2(-2) ………
[using (3)]
Sm+n=-(m+n)
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