Let `n` be a positive integer with `f(n) = 1! + 2! + 3!+.........+n! and p(x),Q(x)` be polynomial in `x` such that `f(n+2)=P(n)f(n+1)+Q(n)f(n)` for all `n >= ,` Then

Let n be a positive integer with f(n) = 1! + 2! + 3!+.........+n! and p(x),Q(x) be polynomial in x such that f(n+2)=P(n)f(n+1)+Q(n)f(n) for all n >=1 , Then p(2)=

Let n be a positive integer with f(n) = 1! + 2! + 3!+.........+n! and p(x),Q(x) be polynomial in x such that f(n+2)=P(n)f(n+1)+Q(n)f(n) for all n >= 1, Then (a) P(x) = x+3 (b) Q(x) = -x-2 (c) P(x) = -x-2 (d) Q(x) = x+3

Let n be a positive integer with f(n)=1!+2!+3!+….+n! and P(x) and Q(x) be polynomials in x such that f(n+2) = Q(n)f(n) + P(n)f(n+1) . Find P(2).

Let f : N rarr R be a function such that f(1) + 2f(2) + 3f(3) + ....+nf(n)= n(n+1) f(n) , for n ge 2 and f(1) = 1 then

Let f : N rarr R be a function such that f(1) + 2f(2) + 3f(3) + ....+nf(n)= n(n+1) f(n) , for n ge 2 and f(1) = 1 then

f(x)=e^(-(1)/(x)), where x>0, Let for each positive integer n,P_(n) be the polynomial such that (d^(n)f(x))/(dx^(n))=P_(n)((1)/(x))e^(-(1)/(x)) for all x>0. show that P_(n+1)(x)=x^(2)[P_(n)(x)-(d)/(dx)P_(n)(x)]

Let f : N rarr N be defined as f(x) = 2x for all x in N , then f is

Let f : N rarr N be defined as f(x) = 2x for all x in N , then f is

If f(x) is a polynomial of degree n such that f(0)=0,f(x)=(1)/(2),...,f(n)=(n)/(n+1) then the value of f(n+1) is

If f(x) is a polynomial of degree n such that f(0)=0 , f(x)=1/2,....,f(n)=n/(n+1) , ,then the value of f (n+ 1) is