For `n in N`, `(4-(2)/(1))(4-(2)/(2))(4-(2)/(3))(4-(2)/(4)).........(4-(2)/(n))` is

If s_(n)=(1-(4)/(1))(1-(4)/(9))(1-(4)/(25))......(1-(4)/((2n-1)^(2))) where n in N, then

lim_(n rarr oo)(((n+1)^(1/3))/(n^(4/3))+((n+2)^(1/3))/(n^(4/3))+.....+((2n)^(1/3))/(n^(4/3))) is equal to

1.4+2.5+.......+n(n+3)=

4^(n)C_(0)+4^(2)(nC_(1))/(3)+4^(3)(nC_(2))/(3)+4^(4)(nC_(3))/(4)+....+4^(n+1)(nC_(n))/(n+1) is equal to

4C_(0)+(4^(2))/(2)*c_(1)+(4^(3))/(3)c_(2)+............+(4^(n+1))/(n+1)C_(n)=(5^(n+1)-1)/(n+1)

Prove that: (1)/(2)nC_(1)-(2)/(3)nC_(2)+(3)/(4)nC_(3)-(4)/(5)nC_(4) +....+((-1)^(n+1)n)/(n+1)*nC_(n)=(1)/(n+1)

(2^(2)*c_(0))/(1.2)+(2^(3)*C_(1))/(2.3)+(2^(4)*c_(2))/(3.4)+......+(2^(n+2)*C_(n))/((n+1)(n+2))=

1+((log n)^(2))/(2!)+((Log n)^(4))/(4!)+...... oo =

Find lim_(n rarr oo)S_(n); if S_(n)=(1)/(2n)+(1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-4))+......+(1)/(sqrt(3n^(2)+2n-1))

If omega is a complex cube root of unity,then the value of the expression 1(2-omega)(2-omega^(2))+2(3-omega)(3-omega^(2))+...+(n-1)(n-omega)(n-omega^(2))(n-omega^(2))(n>=2) is equal to (A) (n^(2)(n+1)^(2))/(4)-n( B) (n^(2)(n+1)^(2))/(4)+n( C) (n^(2)(n+1))/(4)-n(D)(n(n+1)^(2))/(4)-n