Question

{(1/sqrt(2))^n} from n=0 to infinity; is the series convergent or divergent? if convergent, why? and sum?

Answer 1

The series is convergent.
Step-by-step explanation:
`\lim_(n \to \infty) (1)/( 2^(n) ) =` 1/∞ = 0 ( it would be divergent if the answer was: -∞ or +∞ )
Sum of the infinite geometric series:
S∞ = a1 / ( 1-r )
a1 = 1 a2=
`(1)/( √(2) )` , a3=1/2, a4=
`(1)/(2 √(2) )`...
r =
`(1)/( √(2) )`
S∞ =