The sum of the infinte series `sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)/(sqrt(6)))+....sin^(-1)((sqrt(n)-sqrt(n-1))/(sqrt(n(n+1))))`

The sum of the infinite series "sin"^(-1)((1)/(sqrt2))+"sin"^(-1)((sqrt2-1)/(sqrt6))+"sin"^(-1)((sqrt3-sqrt2)/(sqrt12))+…+…+"sin"^(-1)((sqrtn-sqrt((n-1)))/(sqrt(n(n+1))))+… is

Find the sum of infinite series : S = sin^-1(1/sqrt2) + sin^-1((sqrt2 -1)/sqrt6) + sin^-1((sqrt3 - sqrt2)/sqrt12) + ...... infty

The sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+ . . . . .+(1)/(sqrt(n^(2)-1)+sqrt(n^(2))) equals

The sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+ . . . . .+(1)/(sqrt(n^(2)-1)+sqrt(n^(2))) equals

The sum of n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))+... is

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to

The sum of the first n terms of the series (1)/(sqrt(2)+sqrt(5))+(1)/(sqrt(5)+sqrt(8))+(1)/(sqrt(8)+sqrt(11))+ .... is

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/sqrt(r(r+1))) is equal to