Question

Mth term of an ap is 1/n and nth ter is 1/m ten what is the mn^th term

Answer 1

a+(m-1)d=1/n..................(1)
a+(n-1)d=1/m...................(2)
1-2 we get
(m-n)d=-1/m+1/n
d=1/mn
substituting in (1)
a+(m-1)1/mn=1/n
a+ 1/n - 1/mn=1/n
a=1/mn
mn term of series is
=1/mn+(mn-1)1/mn
=1