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` `(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-ax)(1-bx)] is a a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+..., then a_(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)

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

(lim_(x rarr a)(x^(n)-a^(n))/(x-a) is equal to na^(n)b*na^(n-1) c.nad.1

Show that: (a+(1)/(b))^(m)x(a-(1)/(b))^(n)(b+(1)/(a))^(m)x(b-(1)/(a))^(n)=((a)/(b))^(m+n)

If (1+x-x^2)^n/(1+x^2)=a_0+a_1x+a_2x^2+...+a_(2n)x^(2n) then find a_0-a_1+a_2_...+a_(2n)

If (1+x-x^2)^n/(1+x^2)=a_0+a_1x+a_2x^2+...+a_(2n)x^(2n) then find a_1+a_3+a_5+...+a_(2n-1)

If (1+2x-x^2)^n/(1+x^2)=a_0+a_1x+a_2x^2+...+a_(2n)x^(2n) then find a_0+a_2+a_4+...+a_(2n)

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

(d^(n))/(dx^(n))(log x)=(a)((n-1)!)/(x^(n))(b)(n!)/(x^(n))(c)((n-2)!)/(x^(n))(d)(-1)^(n-1)((n-1)!)/(x^(n))