If `f(n)=1^2+2.2^2+3^2+2.4^2+5 .6^2+2.6^2+...+ n` terms ,then (A) `f(n)= (n(n+1)^2)/2`, if n is even (B) `f(n)= (n^2(n+2)^2)/2, if n is even (C) `f(n)= (n^2(n+1))/2`, if n is odd (D) f(n)= (n(n+3)^2)/2` if n is odd

Let f : N to N : f (n) = {underset((n)/(2), " when n is even ")( (1)/(2) (n+1) , " when n is odd ") Then f is

If f:{1,2,3...}rarr{0,+-1,+-2...} is defined by f(n)={(n)/(2), if n is even -((n-1)/(2)) if n odd } then f^(-1)(-100) is

Let f_(1),f_(2),f_(3)...... be a sequence of integers satisfying f_(n-1)+f_(n)=2n for all n>=2 .If f_(1)=100 then (A) "f_(n)=n+98" if "n" is odd (B) "f_(n)=n-98" if "n" is even (C) "f_(n)=n+99" if "n" is odd (D) "f_(n)=n-99" if "n" is even

f_(n)={{:(f_(n-1)" if n is even"),(2f_(n-1)" if n is odd"):} and f_(o)=1 , find the value of f_(4)+f_(5)

If f(1) = 1 and f(n + 1) = 2 f(n) + 1, if n ge 1, then f(n) is.

Given f(1)=2 and f(n+1)=(f(n)-1)/(f(n)+1)AA n in N then

Number of ways in which three numbers in A.P.can be selected from 1,2,3,...,n is a.((n-1)/(2))^(2) if n is even b.n(n-2)/(4) if n is even c.((n-1)^(2))/(4) if n is odd d.none of these

f (1) = 1, n> = 1f (n + 1) = 2f (n) +1 then f (n) =

lim_ (n rarr oo) ((n) / (n ^ (2) +1) + (n) / (n ^ (2) +2) + (n) / (n ^ (2) +3) +. .. (n) / (n ^ (2) + n))