Question

If the nth term of an ap is 1/n and nth term is 1/m then find the sum to mn terms

Answer 1

Step-by-step explanation:

If mth term of an A.P is 1/n and the nth term is 1/m. If mth term of an A.P is 1/n and the nth term is 1/m show that the sum of mn term is 1/2(mn+1).

Answer 2

Answer:

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