Question

If mth term of an A.P is and nth
term of the A.P is
mnth term is 1.
then show that​

Answer 1

Step-by-step explanation:

Given, am=n

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

and, an=m

a+(n-1)d=1/m......2

subtracting equation 1 from 2 we get,

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

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

- - -

___________

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

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

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

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

d=1/mn............3

putting the value of equation 3 on equation 1

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

a+(m-1) × 1/mn =1/n

a+m×1/mn- 1×1/mn=1/n

a+1/n-1/mn=1/n

a-1/mn=1/n-1/n

a-1/mn=0

a=1/mn.........4

therefore,

amn=a+(mn-1)d

=1/mn+(mn-1)×1/mn. [by eq. 3and 4]

=1/mn+mn×1/mn- 1/mn

=1/mn+1-1/mn

amn = 1

hence ,it is prooved.

thank u..