​ Find the sum of the GP : √2 + 1/√2 + 1/2√2 + ..... to 8 terms ​

Question

Find the sum of the GP :

√2 + \(\frac{1}{√2} + \frac{1}{2√2} + .... \) to 8 terms

Answer 1

Sum of a G.P. series is represented by the formula, S_n = a\(\frac{1-r^n}{1-r}\), when |r|<1. 

‘Sn’ represents the sum of the G.P. series up-to nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.

Here,

a = \(\sqrt{2}\)

r = (ratio between the n term and n-1 term) \(\frac{1}{\sqrt{2}} \div \sqrt{2} = \frac{1}{2}\)

n = 8 terms