Question

mth term = 1/n , nth term = 1/m show (mn)th term = 1​

Answer 1

am=a+(m-1)d

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

an=a+(n-1)d

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

subtract equation 1 and 2

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

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

1/mn=d equation (3)

now in equation first put value of d(common difference)

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

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

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

-a=-1/mn

a=1/mn equation( 4)

from equation 3 and 4

value of a=1/mn

value of d=1/mn

(mn)the term =??

formula - a(n)=a+(n-1)*d

put value

=1/mn+(mn-1)*1/mn

=1/mn+1-1/mn

=1

hence proved

thanks hope its helpful