0 votes 0 votes What is the coefficient of $x^{12}$ in the power series of $\dfrac{x^3}{(1+2x)^2}?$ Set Theory & Algebra generating-functions + – Kaluti asked Feb 1, 2018 • recategorized Jun 14, 2022 by Arjun Kaluti 633 views answer comment Share Follow See all 8 Comments See all 8 8 Comments reply Kaluti commented Feb 1, 2018 reply Follow Share i am getting 5120 answer 0 votes 0 votes sumit goyal 1 commented Feb 1, 2018 reply Follow Share - 5120 will be answer 1 votes 1 votes gauravkc commented Feb 1, 2018 reply Follow Share Can someone post solution :) 0 votes 0 votes Inspiron commented Feb 1, 2018 reply Follow Share What is the answer given? I am getting very different from above mentioned. 0 votes 0 votes Shubhanshu commented Feb 1, 2018 reply Follow Share It should be $-5120$. 0 votes 0 votes sumit goyal 1 commented Feb 1, 2018 reply Follow Share use binomial $(x^3) \underbrace{(1+2x)^{-2}}$ find coefficient of $(x^9)$ from 2nd term it will be : $\frac{n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8) \times (2x)^{9}}{9!}$ n = -2 here $\frac{-2(-3)(-4)(-5)(-6)(-7)(-8)(-9)(-10) \times (2x)^{9}}{9!}$ =$- \frac{2(3)(4)(5)(6)(7)(8)(9)(10) \times (2x)^{9}}{9\times 8!}$ = $10(-1) \times 512 x^{9} = -5120$ 0 votes 0 votes Kaluti commented Feb 2, 2018 reply Follow Share but here n = 2 na 0 votes 0 votes sumit goyal 1 commented Feb 2, 2018 reply Follow Share why n=2 , i took denominator above so it becomes -2 0 votes 0 votes Please log in or register to add a comment.
Best answer 1 votes 1 votes Hope This helps Pawan Kumar 2 answered Feb 2, 2018 • selected Feb 2, 2018 by Kaluti Pawan Kumar 2 comment Share Follow See all 0 reply Please log in or register to add a comment.