[(1)/(2n)+(1)/(3y)=2],[(1)/(32)+(1)/(27)=(13)/(6)]

If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1)/(2n^(2))+(1)/(3n^(3))-……) then lambda=

If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1)/(2n^(2))+(1)/(3n^(3))-……) then lambda=

If y=x^(2)e^(x) ,show that y_(n)=(1)/(2)n(n-1)y_(2)-n(n-2)y_(1)+(1)/(2)(n-1)(n-2)}

If lta_(n)gtandltb_(n)gt be two sequences given by a_(n)=(x)^((1)/(2^(n)))+(y)^((1)/(2^(n))) and b_(n)=(x)^((1)/(2^(n))) -(y)^((1)/(2^n)) for all ninN . Then, a_(1)a_(2)a_(3) . . . . .a_(n) is equal to

If lta_(n)gtandltb_(n)gt be two sequences given by a_(n)=(x)^((1)/(2^(n)))+(y)^((1)/(2^(n))) and b_(n)=(x)^((1)/(2^(n))) -(y)^((1)/(2^n)) for all ninN . Then, a_(1)a_(2)a_(3) . . . . .a_(n) is equal to

If |(x^(n),x^(n+2),x^(n+3)),(y^(n),y^(n+2),y^(n+3)),(z^(n),z^(n+2),z^(n+3))| = (x -y) (y -z) (z -x) ((1)/(x) + (1)/(y) + (1)/(z)) , then n equals

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

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

If H_(n)=1+(1)/(2)+(1)/(3)+...+(1)/(n), then value of 1+(3)/(2)+(5)/(3)+...+(2n-1)/(n) is

For natural numbers m , n if (1-y)^(m)(1+y)^(n)=1+a_(1)y+a_(2)y^(2)+a_(3)y^(3)+.....,anda_(1)=a_(2)=10 , then-