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If sum of n term is m and sum of m term is n than prove that sum of m+n term is equal to -(m+n)

Posted by Aman Kumar 5 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 11 months ago

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

S n= 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 = 2 n - 2 m

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)

Hence Proved.

1Thank You

ANSWER

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