Question

If the term of an A. p. is 1/n and the nth term is 1/m,then prove that the sum to terms is mn+1/2

Answer 1

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Answer 2

Answer:

$a + (m)d = \frac{1}{m} \\ \\ a + (m)d = \frac{1}{n} \\ \\ \frac{1}{n} - \frac{1}{m} = (m + 1 - n - 1) \\ \\ \frac{m - n}{mn} = (m + n)d \\ \\ (d = \frac{1}{mn})(a = \frac{1}{mn}) \\ \\ mn = a + (mn - 1)d \\ \\ \frac{1}{mn} + \frac{mn - 1}{mn} = 1$