If the Mth term of an AP be 1/N and its Nth term be 1/M then show that its (MN)th term is 1.

If the Mth term of an AP be 1/N and its Nth term be 1/M then show that

1.	If the Mth term of an AP be 1/N and its Nth term be 1/M then show that its (MN)th term is 1.
Answer» tnx bhai.... Given that, mth term=1/n and nth term=1/m.then ,let a and d be the first term and the common difference of the A.P.so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).subtracting equation (1) by (2) we get,md-d-nd+d=1/n-1/m=>d(m-n)=m-n/mn=>d=1/mn.\xa0again if we put this value in equation (1) or (2) we get, a=1/mn.then, let A be the mnth term of the APa+(mn-1)d=1/mn+1+(-1/mn)=1\xa0hence proved.