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Find the sum of each of the following infinite series : `sqrt(2)-1/sqrt(2)+1/(2sqrt(2))-1/(4sqrt(2))+...oo`

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Find the sum of each of the following infinite series :
`sqrt(2)-1/sqrt(2)+1/(2sqrt(2))-1/(4sqrt(2))+...oo`
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Correct Answer - `8(2+sqrt(2))`
`a=8 and r=(4 sqrt(2))/8=1/sqrt(2)`
`:. S=a/((1-r))=8/((1-1/sqrt(2)))=(8sqrt(2))/((sqrt(2)-1))xx((sqrt(2)+1))/((sqrt(2)+1))=8(2+sqrt(2))`.
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