Question

plz solve it.............​

Answer 1

$given \: that \: \\ \: \: \: a + (m - 1)d = \frac{1}{n} \: \: \: ....(1) \\ \: \: \: a + (n - 1)d = \frac{1}{m} \: \: \: ....(2) \\ - \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: (subtracting) \\ d(m - n) = \frac{1}{n} - \frac{1}{m} \\ d(m - n) = \frac{(m - n)}{mn} \\ d = \frac{1}{mn} \\ putting \: d \: value \: in \: any \: equation \: gives \\ a = \frac{1}{mn} \\ \\ now \: mn \: term = \\ a + (mn - 1)d \\ putting \: values \\ \frac{1}{mn } + ( mn - 1)( \frac{1}{mn} ) \\ = \frac{1}{mn} + 1 - \frac{1}{mn} \\ = 1 - 1 = 0$