Find an explicit formula (in terms of `n epsilon N` ) for `f(n)=f(n-1)+2n-1`.

find the sum of n terms: a(n) = n(n+1)-2

If f:N rarr N is defined by f(n)=n-(-1)^(n), then

The n^(th) term, an of a sequence of numbers is given by the formula a_n = a_(n – 1) + 2n for n ge 2 and a_1 = 1 . Find an equation expressing an as a polynomial in n. Also find the sum to n terms of the sequence.

Let f: N to R be a function satisfying the condition f(1) + f(2) ……………. +f(n) = n^(2) f(n) AA n in N If f(2025) = 1/(2026) , then f(1) = ………….

A Function f is defined for all positive integers and satisfies f(1)=2005 and f(1)+f(2)+.........+f(n)=n^(2)f(n) for all n>1. Find the value of f(2004)

A mapping f:N rarr N where N is set of natural numbers is destined as f(n)=n^(2),n=odd and 2n+1,n= even for n in N then f is

Let f(n) = [(1)/(2) + (n)/(100)] where [n] denotes the integral part of n. Then the value of sum_(n=1)^(100) f(n) is

Consider the function f defined on the set of all non-negative interger such that f(0) = 1, f(1) =0 and f(n) + f(n-1) = nf(n-1)+(n-1) f(n-2) for n ge 2 , then f(5) is equal to

Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^(2)+5((2n+1)/(2n-1))^(3)+