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Let T(n)=(1)/((sqrt(n)+sqrt(n+1))(4sqrt(...

Let `T_(n)=(1)/((sqrt(n)+sqrt(n+1))(4sqrt(n)+4sqrt(n+1)))` and `S_(n)=sum_(r=1)^(n)T_(r)` then find `S_(15)`.

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The correct Answer is:
1
`T_(n)=(root(3)(n)-root(4)((n+1)))/((sqrt(n)+sqrt(n+1))(sqrt(n)-sqrt(n+1)))=root(4)((n+1))-root(4)(n)`
`T_(1)=root(4)(2)-1`
`T_(2)=root(4)(3)-root(4)(2)`
`T_(n)=root(4)(n+1)-root(4)(n)`
`S_(n)=root(4)(n+1)-1`
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