Suppose that F(n + 1) =`(2F(n) + 1)/2` for n = 1,2,3,,,, and F(1) = 2. Then F(101) is

If f(n + 1) = (2f(n) + 1)/2 , n = 1,2,3,....... and f(1) = 2, then find the value of f(101)

If f(n+1)=(2f(n)+1)/(2),n=1,2,3,... and f(1)=2 then find the value of f(101).

A mappin f : N rarrN where N is the set of natural numbers is defined as f(n)=n^(2) for n odd f(n)=2n+1 for n even for n inN . Then f is

Given a sequence t_1 , t_2 ,..... if its possible to find a function f(r) such that t_r = f(r + 1) - f(r) then sum_(r = 1)^n t_r = f(n + 1) - f(1) Sum of the sum_(r = 1)^n r(r + 3)(r + 6) is

f_(n)(x)=e^(f_(n-1)(x))" for all "n in N and f_(0)(x)=x," then "(d)/(dx){f_(n)(x)} is

If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then find f(x).

Show that the function f:N to N, given by f (1) =f (2) =1 and f (x) =x -1, for every x gt 2, is onto but not one-one.

Let N be the set of natural numbers and two functions f and g be defined as f, g : N to N such that : f(n)={((n+1)/(2),"if n is odd"),((n)/(2),"if n is even"):}and g(n)=n-(-1)^(n) . The fog is :

Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f_1,0)a n d(f_2,0) where f_1>0a n df_2<0. Let P_1a n dP_2 be two parabolas with a common vertex at (0, 0) and with foci at (f_1 .0)a n d (2f_2 , 0), respectively. Let T_1 be a tangent to P_1 which passes through (2f_2,0) and T_2 be a tangents to P_2 which passes through (f_1,0) . If m_1 is the slope of T_1 and m_2 is the slope of T_2, then the value of (1/(m_1^ 2)+m_2^ 2) is

If f is a function such that f(0)=2,f(1)=3,a n df(x+2)=2f(x)-f(x+1) for every real x , then f(5) is 7 (b) 13 (c) 1 (d) 5