Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the sum of the coefficients of all even powers of x in the product <img alt="(1+x+x^{2}+....+x^{2n})(1-x+x^{2}-x^{3}+....+x^{2m})" src="/latex-image/?%281&plus;x&plus;x%5E%7B2%7D&plus;....&plus;x%5E%7B2n%7D%29%281-x&plus;x%5

If the sum of the coefficients of all even powers of x in the product (1+x+x^{2}+....+x^{2n})(1-x+x^{2}-x^{3}+....+x^{2m}) is 61, then n is equal to _________.
Option: 1 30
Option: 260
Option: 315
Option: 4 45
 

Answers (1)

best_answer

\text { Let } (1+x+x^{2}+....+x^{2n})(1-x+x^{2}-x^{3}+....+x^{2n})=a_{0}+a_{1} x+a_{2} x^{2}+\ldots \ldots

\\Put \,\, x=1 \\ (2 n+1).1 =a_{0} + a_{1} + a_{2}+ \ldots \ldots \\ Put\, x =-1 \\ 1.(2 n+1)= a_{0} - a_{1} + a_{2}+\ldots \ldots \\ From (i)+(ii) \\ 4 n+2 =2 (a_{0}+a_{2}+\ldots ) \\ So,\,\, 2 n+1=61 \\ \Rightarrow n=30

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 registration ends tomorrow; changes introduced in exam this year
anam-khan

BTech Admission 2025 Live: JEE Mains registrations closing tomorrow; VITEEE, MET exam dates out
anam-khan

JEE Main 2025 Live: NTA to close JEE registration on Friday; apply at jeemain.nta.nic.in, correction window

Latest Question