Question

If the m term of an AP be 1/n and n term be 1/m then show that it's mn term is 1​

Answer 1

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)

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 mn th term of the AP

a+(mn-1)d=1/mn+1+(-1/mn)=1

hence proved

Step-by-step explanation: