The cofficient of `x^n` in `x/((x-a)(x-b))` is `(a^n-b^n)/(a-b)xx 1/(a^n b^n)`

If the expansion in powers of x of the function 1//[(1-a x)(1-b x)] is a a_0+a_1x+a_2x^2+a_3x^3+ ,then coefficient of x^n is (b^n-a^n)/(b-a) b. (a^n-b^n)/(b-a) c. (b^(n+1)-a^(n+1))/(b-a) d. (a^(n+1)-b^(n+1))/(b-a)

If a\ a n d\ b are the coefficients of x^n in the expansions of (1+x)^(2n) and (1+x)^(2n-1) respectively, find a/b .

If A and B are the coefficients of x^n in the expansion (1 + x)^(2n) and (1 + x)^(2n-1) respectively, then A/B is

If the expansion in powers of x of the function 1//[(1-a x)(1-b x)] is a a_0+a_1x+a_2x^2+a_3x^3+ ,t h e na_n i s a. (b^n-a^n)/(b-a) b. (a^n-b^n)/(b-a) c. (b^(n+1)-a^(n+1))/(b-a) d. (a^(n+1)-b^(n+1))/(b-a)

If the expansion in powers of x of the function 1/[(1-a x)(1-b x)] is a a_0+a_1x+a_2x^2+a_3x^3+ ,t h e na_n i s a. (b^n-a^n)/(b-a) b. (a^n-b^n)/(b-a) c. (b^(n+1)-a^(n+1))/(b-a) d. (a^(n+1)-b^(n+1))/(b-a)

(b) int(x^(n-1)dx)/(sqrt(a^n+x^n))

If y=(x-a)^(m)(x-b)^(n) , prove that (dy)/(dx)=(x-a)^(m-1)(x-b)^(n-1)[(m+n)x-(an+bm) ].

(d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

Prove that (x+b)^(n)=""^(n)C_(0) x^(n)+""^(n)C_(1) x^(n-1)b+ ""^(n)C_(2) x^(n-2) b^(2)+...+ ....+..... ""^(n)C_(n) b^(n), and n in N and hence find (101)^(4) .