Q89.
It's given that (1+x)^n=nC0+nC1x+nC2x^2+...+nCnx^n....(*)
Where n is a positive integer
By differentiating both sides of(*)with respect to x,find the value of 100C1-2 100C2+3 100C3+...-100 100C100
Q90
Consider the geometric sequence
1,(x-1)^3,(x-1)^6,(x-1)^9,...,(x-1)^3n
Where 1<x<2 and n is a non-negative integer
Let S(n)=1+(x-1)^3+(x-1)^6+(x-1)^9+...+(x-1)^3n
a) Express S(lim) in terms of x
b)Let T(n)=3/2^2+6/2^5+9/2^8+...+3n/2^(3n-1)
Thanks