Question

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)

Answer 1

HELLO DEAR,



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 

Answer 2

Answer:

Therefore, Am = a+ (m-1)d=1/n ….(i)

An = a+(n-1)d=1/m ….(ii)

Subtracting equation (ii) from (i)

d[(m-1)-(n-1)] = 1/n-1/m,

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

d = 1/mn ….(iii)

Substituting equation (iii) in (i)

a+(m-1)/mn = 1/n,

a = 1/n[1-(m-1)/m],

a = 1/mn ….(iv)

Now Amn i.e the mnth term of AP = a+(mn-1)d,

Explanation: