If `f(n+1)=(2F(n)+1)/2,n=1,2,3,.... a n d` `F(1)=2.` Then `F(101)` equals 52 (b) 49 (c) 48 (d) 51

Suppose that F(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 a n dF(1)=2. T h e ndotF(101) equals a. 50 b. 52 c. 54 d. none of these

For each positive integer n , let f(n+1)=n(-1)^(n+1)-2f(n) and f(1)=(2010)dot Then sum_(k=1)^(2009)f(K) is equal to 335 (b) 336 (c) 331 (d) 333

If f(x)=log((1+x)/(1-x))a n dt h e nf((2x)/(1+x^2)) is equal to {f(x)}^2 (b) {f(x)}^3 (c) 2 f(x) (d) 3f(x)

If D_k=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum_(k=1)^n D_k=48 ,then n equals (a) 4 (b) 6 (c) 8 (d) none of these

If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetrical about the y-axis ,then n equals (a)2 (b) 2/3 (c) 1/4 (d) 1/3

If f(x) = a(x^n +3), f(1) = 12, f(3) = 36 , then f(2) is equal to

f(x) is a continuous function for all real values of x and satisfies int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot Then int_(-3)^5f(|x|)dx is equal to (19)/2 (b) (35)/2 (c) (17)/2 (d) none of these

f(x) is a continuous function for all real values of x and satisfies int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot Then int_(-3)^5f(|x|)dx is equal to (19)/2 (b) (35)/2 (c) (17)/2 (d) none of these

f(1)=1 and f(n)=2sum_(r=1)^(n-1) f (r) . Then sum_(n=1)^mf(n) is equal to (A) 3^m-1 (B) 3^m (C) 3^(m-1) (D)none of these