Question

the sum is shown in the picture ​

Answer 1

Step-by-step explanation:

Given :-

1/[1+(a^(m-n))] + 1/[1+(a^(n-m))]

To find:-

Prove that 1/[1+(a^(m-n))] + 1/[1+(a^(n-m))] = 1

Solution :-

On taking LHS :

1/[1+(a^(m-n))] + 1/[1+(a^(n-m))]

=> 1/[1+(a^m/a^n)] +1/[1+(a^n/a^m)]

=> 1/[(a^n+a^m)/a^n] + 1/[(a^m + a^n )/a^m]

=> [(a^n)/(a^m + a^n )] + [(a^m)/(a^m + a^n)]

=> (a^n + a^m) /(a^m + a^n)

=> (a^m + a^n)/(a^m + a^n)

=> 1

=> RHS

=> LHS = RHS

Hence, Proved.

Answer:-

1/[1+(a^(m-n))] + 1/[1+(a^(n-m))] = 1

Used formulae:-

• a^m / a^n = a^(m-n)
• 1/(1/a) = a

Answer 2

Answer:

please mark as branlist answer