Then find the value

Question

Answer 1

x = 1 + 2^1/6  + 2^2/6 + 2^3/6 + 2^4/6 + 2^5/6

Clearly, This is a Geometric Progression with 

Common Difference (r) = 2^1/6

First Term (a) = 1

Number Of Terms (n) = 6

And since we know the formula for the sum of GP, which is:

S= a(rⁿ-1)/r-1

S = ((2^1/6)⁶ - 1)/2^1/6-1

S(x) = 1/2^1/6-1

Now, We have to find,

(1+1/x)³⁰ or (1 + 2^1/6 -1)³⁰

⁼ (2^1/6)³⁰

⁼ 2⁵ 

=32