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

If f(r)=1+1/2+1/3+1/ra n df(0)=0,t h e nsum_(r=1)^n(2r+1)f(r) is equal to (a) nf(n+1)-((n^2-3n+2))/2 (b) (n+1)^2f(n)-((n^2-3n+2))/2 (c) (n+1)^2f(n+1)-((n^2+3n+2))/2 (d) (n+1)^f(n+1)-((n^2-3n+2))/2

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

If f(x) is integrable over [1,2] then int_(1)^(2)f(x)dx is equal to (a) lim_(nto oo) 1/n sum_(r=1)^(n)f(r/n) (b) lim_(nto oo) 1/n sum_(r=n+1)^(2n) f(r/n) (c) lim_(nto oo) 1/n sum_(r=1)^(n)f((r+n)/n) (d) lim_(nto oo) 1/n sum_(r=1)^(2n)f(r/n)

If alpha and beta are roots of equation x^2 +px +q = 0 and f(n) = alpha^n+beta^n , then (i) f(n+1)+pf(n) -qf(n-1)=0 (ii) f(n+1)-pf(n) +qf(n-1)=0 (iii ) f(n+1)+pf(n) +qf(n-1)=0 (iv) f(n+1)-pf(n) -qf(n-1)=0

Let sum_(r=1)^(n) r^(6)=f(n)," then "sum_(n=1)^(n) (2r-1)^(6) is equal to

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

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

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