If `1.1!+2.2!+3.3!+...+n*n!``=k` for `n=15`, then the value in the units place of, k is

If 1+n+n^(2)+...+n^(127)=(1+n+n^(2)+...+n^(63))(n^(k)+1) ,then the value of k is

If (1.5)^(30)=k, then the value of sum_((n=2))^(29)(1.5)^(n) is :

f : N -> R be a function satisfying the following conditions: f(1)=1 and f(1)+2.f(2)+3.f(3)+........n.f(n)=n(n+1)f(n) for n>=2 The value of f(1003) is (1)/(K) ,where K equals

If the middle term in the expreansion of (1+x)^(2n) is ([1.3.5….(2n-1)])/(n!) (k) , where n is a positive integer , then k is .

Let a=3(1)/(233)+1 and for all n>=3 let f(n)=C(n,0)a^(n-1)-C(n,1)*a^(n-2)-C(n,2)a^(n-3)-...+(-1)^(n-1)*C(n,n-1) If the value of f(2007)+f(2008)=3^(k) where k in N then the value of k is

If lim_(n->oo)(1(2n-1)^(k)+2(2n-2)^(k)+3(2n-3)^(k)+...+n.n^(k))/(n^(k+1))=(2^(k+a)-2)/(k+1)+(1-2^(k+b))/(k+2) where a, b, k in N and k >= 5 then the value of (a+b)/(3) is