Question

indicate wether the given series is converge or diverge if it converges find the sum from zero to infinity
(1)/(sqrt 7)^k

Answer 1

Sorry lol. Nt very gud in this

Answer 2

in converges for sure

Answer 3

\[\sum_0^{\infty}\frac{1}{\sqrt{7}^k}\] converges because
\[|\frac{1}{\sqrt{7}}|<1\]

Answer 4

use
\[\sum_{k=0}^{\infty}x^k =\frac{1}{1-x}\]
\[\sum_{k=0}^{\infty}\frac{1}{\sqrt{7}^k}=\frac{1}{1-\frac{1}{\sqrt{7}}}\]