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If the mth term of an AP is 1/n and the nth term is 1/m,show the sum of its first (mn)terms is 1/2(mn+1).

Posted by Priyanshu Sharma 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Rita Gokani 6 years, 10 months ago

am=1/n, an=1/m a + (m-1)d = 1/n a + (n-1)d = 1/m By solving we get d=1/mn Also a=1/mn Then, S(mn)=mn/2[2(1/mn)+(mn-1)1/mn] =mn/2[2/mn +1 - 1/mn] =mn/2[2/mn-1/mn+1] =mn/2(1/mn+1) by multiplying =mn/2×1/mn+mn/2+1 LCM =1/2 +mn+2/2 =mn+2/2 =1/2mn +1 Hope u understood

1Thank You

Nanu Parjapat 6 years, 10 months ago

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CBSE > Class 10 > Mathematics