If mth term of an A.P. is - and nth term is, then find the sum of itsf

1.	If mth term of an A.P. is - and nth term is, then find the sum of itsfirst mn terms.
Answer» 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 hence proved. Like my answer if you find it useful!

If mth term of an A.P. is - and nth term is, then find the sum of itsfirst mn terms.

Answer»

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 hence proved.

Like my answer if you find it useful!