The sum of 10 terms of the series `sqrt2 + sqrt6 + sqrt18 +...` is

Explanation

We have given series `sqrt2 + sqrt6 + sqrt18 +...`

This is a G.P. series.

Then the formula for sum of G.P. series `S_n=(a(r^n-1))/(r-1)`

Now here `a=sqrt(2), r=sqrt(3),n=10`

`\Rightarrow S_10=(sqrt(2)((sqrt(3))^10-1))/(sqrt(3)-1)`

`\Rightarrow S_10=(sqrt(2)(3^5-1))/(sqrt(3)-1)`

`\Rightarrow S_10=((sqrt(2)(3^5-1))/(sqrt(3)-1)) \times ((sqrt(3)+1)/(sqrt(3)+1))`

`\Rightarrow S_10=121( √ 6 + √ 2 )`