Question

Ami akta dicchi kor...mth term of a ap is 1/n and nth term of that ap is 1/m..prove that sum of mn term is 1/2*(mn+1)

Answer 1

May this will help you

Answer 2

$tm = \frac{1}{n} \\ a +(m - 1)d = \frac{1}{n} ...........(1) \\tn = \frac{1}{m} \\ a + (n - 1)d = \frac{1}{m} .............(2) \\ from \: (1) \: and \: (2) \\ d = \frac{1}{mn} \\ a = \frac{1}{mn} \\ sum \: of \: mn \: terms = \frac{mn}{2} (2a + (mn - 1)d) = \frac{mn}{2} ( \frac{2}{mn} + (mn - 1) \frac{1}{mn} ) \\ = \frac{1}{2} (2 + mn - 1) = \frac{1}{2} (mn + 1)$