`sum_(k=1)^oo 1/(ksqrt(k+2)+(k+2)sqrt(k))=(2+sqrt2)/a` then value of a is

sum_(k=1)^(360)((1)/(ksqrt(k+1)+(k+1)sqrt(k))) is the ratio of two relative prime positive integers m and n. The value of (m+n) is equal to

If sum_(k=4)^(143)(1)/(sqrt(k)+sqrt(k+1))=a-sqrt(b) then a and b are respectively

If sum_(k=4)^(143) (1)/(sqrt(k)+sqrt(k+1))=a-sqrt(b) then a and b respectively are

If lim_(n rarr oo)(sum_(r=1)^(n)sqrt(r)sum_(r=1)^(n)(1)/(sqrt(r)))/(sum_(r=1)^(n)r)=(k)/(3) then the value of k is

If sum_(k = 1)^(oo) (1)/((k + 2)sqrt(k) + ksqrt(k + 2)) = (sqrt(a) + sqrt(b))/(sqrt(c)) , where a, b, c in N and a,b,c in [1, 15] , then a + b + c is equal to

If sum_(k = 1)^(oo) (1)/((k + 2)sqrt(k) + ksqrt(k + 2)) = (sqrt(a) + sqrt(b))/(sqrt(c)) , where a, b, c in N and a,b,c in [1, 15] , then a + b + c is equal to

a,b are distinct natural numbers that (1)/(a)+(1)/(b)=(2)/(5). If sqrt(a+b)=k sqrt(2), then the value of k is

If int_0^1 (dx)/(sqrt(1 + x) - sqrt(x)) =(ksqrt(2))/(3) , then k is :