Suppose thatF(n+1)=`(2F(n)+1)/2` for n=1,2,3,… and F(1)=2. Then,F(101) equals

Suppose that F(n +1) =( 2f(n)+1)/2 for n = 1, 2, 3,.....and f(1)= 2 Then F(101) equals = ?

Let f: RvecR be a continuous odd function, which vanishes exactly at one point and f(1)=1/2dot Suppose that F(x)=int_(-1)^xf(t)dtfora l lx in [-1,2]a n dG(x)=int_(-1)^x t|f(f(t))|dtfora l lx in [-1,2]dotIf(lim)_(xvec1)(F(x))/(G(x))=1/(14), Then the value of f(1/2) is

IF f(x) =2x^2 +bx +c and f(0) =3 and f (2) =1, then f(1) is equal to

Given F_(1)=1, F_(2)=3 and F_(n)=F_(n-1)+F_(n-2) then F_(5) is

Given F_(1)=1, F_(2)=3 and F_(n)=F_(n-1)+F_(n-2) then F_(3) is ____.

If f(x) satisfies the relation f(x+y)=f(x)+f(y) for all x , y in Ra n df(1)=5,t h e n (a) f(x)i sa nod dfu n c t ion (b) f(x) is an even function (c) sum_(n=1)^mf(r)=5^(m+1)C_2 (d) sum_(n=1)^mf(r)=(5m(m+2))/3

Let N be the set of 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) . Then, fog is

Let f(n)=sum_(k=1)^(n) k^2(n C_k)^ 2 then the value of f(5) equals

A function f from integers to integers is defined as f(n)={(n+3",",n in odd),(n//2 ",",n in even):} Suppose k in odd and f(f(f(k)))=27. Then the value of k is ________