Let `f(n)=1+1/2+1/3++1/ndot` Then `f(1)+f(2)+f(3)++f(n)` is equal to
(a)`nf(n)-1`
(b) `(n+1)f(n)-n`
(c)`(n+1)f(n)+n`
(d) `nf(n)+n`

Let f(n)=2cosn xAAn in N , then f(1)f(n+1)-f(n) is equal to (a) f(n+3) (b) f(n+2) (c) f(n+1)f(2) (d) f(n+2)f(2)

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

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

L e tf(n)=1+1/2+1/3++1/ndot Then show that f(n)=int_0^(pi/2)cot(theta/2)(1-cos^ntheta)d theta

Let f(x) = (x^2 - 1)^(n+1) + (x^2 + x + 1) . Then f(x) has local extremum at x = 1 , when n is (A) n = 2 (C) n = 4 (B) n = 3 (D) n = 5

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

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

If f(x) is integrable over [1,], then int_1^2f(x)dx is equal to ("lim")_(nvecoo)1/nsum_(r=1)^nf(r/n) ("lim")_(nvecoo)1/nsum_(r=n+1)^(2n)f(r/n) ("lim")_(nvecoo)1/nsum_(r=1)^nf((r+n)/n) ("lim")_(nvecoo)1/nsum_(r=1)^(2n)f(r/n)

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