(3)/(2)quad ((2^(n)+2^(n-1))/(2^(n+1)-2^(n))=(3)/(2)

Prove that: sqrt((1)/(4))+(0.01)^(-(1)/(2))-(27)^((2)/(3))=(3)/(2) (ii) (2^(n)+2^(n-1))/(2^(n+1)-2^(n))=(3)/(2)

Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2 (ii)\ (2^n+\ 2^(n-1))/(2^(n+1)-2^n)=3/2

1^(2)C_(1)-2^(2)C_(2)+3^(2)C_(3)-+(-1)^(n-1)n^(2)C_(n)=(1)(n^(2)*2^(n+1))/(n+1)(3)(2^(n+1))/(n-1)

A) |lim_(n rarr oo)((n^((1)/(2)))/(n^((3)/(2)))+(n^((1)/(2)))/((n+3)^((3)/(2)))+....+(n^((1)/(2)))/( n+3(n-1) ^((3)/(2))))=

Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^(2)+5((2n+1)/(2n-1))^(3)+

lim_(n rarr oo)(3^(n+1)+2^(n+2))/(3^(n-1)+2^(n-2)) =

lim_(n rarr oo) [(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+(n+3)/(n^(2)+3^(2))+.....+(1)/(n)]

lim_(n rarr oo) [(n+1)/(n^(2)+1^(2) )+(n+2)/(n^(2)+2^(2))+(n^+3)/(n^(2)+3^(2))+.....1/n] =

Evaluate : underset(n to oo) lim[((1+1^(2)/n^(2)))(1+(2^(2))/(n^(2)))(1+(3^(2))/(n^(2)))…(1+(n^(2))/(n^(2)))]^((1)/(n))