Let `f(1) = 1 and f(n) = 2 underset(r=1)overset(n-1)sumf (r)`. Then, `underset(n=1)overset(m) sumf(n)` is equal to

If k=underset(r=0)overset(n)(sum)(1)/(.^(n)C_(r)) , then underset(r=0)overset(n)(sum)(r)/(.^(n)C_(r)) is equal to

If underset(i=1)overset(n)sum cos^(-1) alpha_(i)=0," then "underset(i=1)overset(n)sum alpha_(i)=

If f(x) = (a^(x))/(a^(x) + sqrt(a)), a gt 0 prove that (i) f(x) + f(1-x) = 1 (ii) underset(k=1)overset(2n-1)sum 2f ((k)/(2n)) = 2n-1 (iii) underset(k=1)overset(2n)sum 2f((k)/(2n+1)) = 2n

underset(r=1)overset(n)sum ( r )/(r^(4)+r^(2)+1) is equal to

If T_( r )=( r )/(r^(4)+4) and S_(n)=underset(r=1)overset(n)sum t_( r ) . Then the value of 37S_(5)-(7)/(26) is equal to

The value of cot[underset(n=1)overset(100)Sigmacot^(-1)(1+underset(k=1)overset(n)Sigma2k)] is

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

If f (x) is a function such that f(x+y)=f(x)+f(y) and f(1)=7" then "underset(r=1)overset(n)sum f(r) is equal to :