If the mth term of an A.P. be 1/n and nth term be 1/m, then show that its (mn)th term is 1.


Here is the answer to your question.
Let a and d be the first term and common difference of A.P.

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Tm = 1/n    &      Tn = 1/m

a +(m-1)d = 1/n

a + (n-1)d = 1/m


(m-n)d = m-n/mn

d = 1/mn  ,     & a = 1/mn

now , Tmn = a +(mn-1)d = 1/mn +(mn-1) x 1/mn

                                              =1 +mn-1 / mn = mn/mn = 1.....hence prooved!!

hope ths hlps u ..!!

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