Sum the following geometric series to infinity:
`(a)(sqrt(2)+1)+1+(sqrt(2)-1).............+oo`
`(b)1/2+1/(3^3)+1/(2^3)+1/(3^4)+1/(2^5)+1/(3^6)..........+oo`

Explanation

`(i)`Given,
`(sqrt(2)+1)+1+(sqrt(2)-1).............+oo`

`r=(sqrt(2)-1)` and `a=(sqrt2+1)`

sum of infinite series is `a/(1-r)`

`=>(sqrt(2)+1)/(1-(sqrt(2)-1))`

`=>(sqrt(2)+1)/(2-sqrt(2))`

`=>(sqrt(2)+1)/(2-sqrt(2))xx(2+sqrt(2))/(2+sqrt(2))`

`=>(4+3sqrt2)/(4-2)`

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