[Ex.2:,A={(1)/(x)/x in N,x<8}],[,B={(1)/(2x)/x in N,x<=8}" Find "A-B" and "B-A]

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

From the relation 1+x+x^(2)+* * * + x^(n-1)=(1-x^(n))/(1-x) , find the sum of the series 1+2x+3x^(2)+* * * +(n-1)x^(n-2) .

lim_(x rarr1)((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^(2)),n in N, equals ^2nP_(n)(b)^(2n)C_(n)(c)(2n)!(d) none of these

lim_(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^(2)), n in N , equals

lim_(x rarr0^(-))([x]+[x^(2)]+[x^(3)]++[x^(2n+1)]+n+1)/(1+[x^(2)]+|x|+2x),n in N

The value of lim_(x rarr0)((1+x)^((1)/(x))-e+(1)/(2)ex)/(x^(2)) is

Evaluate lim_(xto0) ((1+x)^(1//x)-e+(1)/(2)ex)/(x^(2)) .

Prove,by induction,that (nC_(0))/(x)-(nC_(1))/(x+1)+(nC_(2))/(x+2)-.........+(-1)^(n)*(nC_(n))/(x+n)=(n!)/(x(x+1)(x+2)......(x+n)),x in

f(x)=e^(-1/x),w h e r ex >0, Let for each positive integer n ,P_n be the polynomial such that (d^nf(x))/(dx^n)=P_n(1/x)e^(-1/x) for all x > 0. Show that P_(n+1)(x)=x^2[P_n(x)-d/(dx)P_n(x)]