CBSE 2012 QUESTION
IF the mth term of AP is 1/n and the nth term is 1/m the sum of mn terms is 1/2(mm+1)
IF the mth term of AP is 1/n and the nth term is 1/m the sum of mn terms is 1/2(mm+1)
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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.
again
if we put this value in equation (1) or (2)
we get, a=1/mn.
then,
let A be the mnth term of the AP
a+(mn-1)d=1/mn+1+(-1/mn)=1