If `a_(n) = sqrt(1+(1+(1)/(n))^(2))+sqrt(1+(1-(1)/(n))^(2))` then value of `overset(20)underset(n=1)sum(1)/(a^(n))` is

If a_(n) = sqrt(1+(1+(1)/(n))^(2))+sqrt(1+(1-(1)/(n))^(2)) then value of sum_(n=1)^(20) (1)/(a^(n)) is

Equation x^(n)-1=0,ngt1,ninN, has roots 1,a_(1),a_(2),...,a_(n),. The value of underset(r=2)overset(n)sum(1)/(2-a_(r)), is

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

Let S _(n ) = sum _( k =0) ^(n) (1)/( sqrt ( k +1) + sqrt k) What is the value of sum _( n =1) ^( 99) (1)/( S _(n ) + S _( n -1)) ?=

The value of lim_(n to oo)sum_(r=1)^(n)(1)/(n) sqrt(((n+r)/(n-r))) is :

If x = sqrt((n-1)/(n+1)) , find the value of (x/(x-1))^2+(x/(x+1))^2

underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-n^(2)) is equal to

If sum_(r=1)^(n) r(sqrt(10))/(3)sum_(r=1)^(n)r^(2),sum_(r=1)^(n) r^(3) are in G.P., then the value of n, is

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n) (a) underset(0)overset(1)intx^(n-1)(1+x)^(n)dx (b) underset(1)overset(2)intx^(n)(x-1)^(n-1)dx (c) underset(1)overset(2)int(1+x)^(n)dx (d) underset(0)overset(1)int(1-x)^(n)x^(n-1)dx

underset(r=1)overset(n-1)(sum)cos^(2)""(rpi)/(n) is equal to