Find the sum of the series `sum_(r=11)^(99)(1/(rsqrt(r+1)+(r+1)sqrtr))`

Explanation

`T_(r)=1/(sqrtrsqrt(r+1)[sqrtr+sqrt(r+1)])=(sqrt(r+1)-sqrtr)/(sqrtrsqrt(r+1))`
`=1/sqrtr-1/(sqrt(r+1))`
=V( r)-V(r+1), where V(r )=`1/(sqrtr)`
`therefore` Required sum, `sum_(r=1)^(99)(V(r )-V(r+1))=V(1)-V(100)`
`=1-1/(sqrt(100))`
`=1-1/10=9/10`