Let `S=sum_(n=1)^(9999)1/((sqrt(n)+sqrt(n+1))(n4+n+1 4))` , then `S` equals ___________.

sum_(n=1)^(oo)(1)/(sqrt(n)+sqrt(n+1))

If S=sum_(n=1)^(9999)(1)/((sqrtn+sqrt(n+1))(root4(n)+root4(n+1))) , then the value of S is equal to

sum_(n=9)^(575)((1)/(n sqrt(n+1)+(n+1)sqrt(n)))=

If S=sum_(n=1)^(10)(2n+(1)/(2)), then S

Let S_(n)=sum_(r=1)^(oo)(1)/(n^(r)) and sum_(n=1)^(k)(n-1)S_(n)=5050, then k=

If S(n)=sum_(k=1)^(n)(k)/(k^(4)+(1)/(4)), then (221S(10))/(10) is equal to:

If the value of lim_(n to oo) (n^(-3//2)) . sum_(j=1)^(6n)sqrt(j) is equal to sqrt(N) , then the value of N is________.

Let sum_(r=1)^(n)r^(4)=f(n)," then " sum_(r=1)^(n) (2r-1)^(4) is equal to

sum_(n=1)^(oo)((1)/(4n-3)-(1)/(4n-1))=(pi)/(n) find n