st","extracted_subject":"MATH","extracted_chapter":"BINOMIAL THEOREM AND MATHEMATICAL INDUCTION","extracted_topic":"BINOMIAL THEOREM FOR ANY INDEX","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1987.png?top_left_x=0&top_left_y=597&width=532&height=265&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f29d","slug":"if-1-x-2-xsup2supsup20sup-asub0sub-asub1subx-asub2","content":"If (1+ x + 2 x²)²⁰ = a₀ + a₁x + a₂x² + ....... + a₄₀ x⁴⁰ fud a₁ + a₃ + a₅ + ........ + a₃₇ + a₃₉ =","options":[{"_id":"68a3829a7f15af4716b73cc9","text":"\$\\frac{4^{20}}{2}\$","sequence":0,"isCorrect":false},{"_id":"68a3829a7f15af4716b73cca","text":"\$\\frac{4^{20}–2^{20}}{2}\$","sequence":1,"isCorrect":true},{"_id":"68a3829a7f15af4716b73ccb","text":"\$\\frac{2^{20}}{2}\$","sequence":2,"isCorrect":false},{"_id":"68a3829a7f15af4716b73ccc","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"$$\\frac{4^{20}–2^{20}}{2}$","explanation":"Put x = 1, x = – 1 and subtract then\n\n(4)²⁰ – 2²⁰\n\n= 2[a₁ + a₃ + ......+a₃₉]","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.505Z","__v":0,"vector_store_id":"6a0f9208-8595-4db9-9e56-79ce99a711a0","updated_at":"2024-08-30T21:49:38.505Z","isStarred":false},"params":{"questionSlug":"if-1-x-2-xsup2supsup20sup-asub0sub-asub1subx-asub2"}}]}]]

Question: If (1+ x + 2 x<sup>2</sup>)<sup>20</sup> = a<sub>0</sub> + a<sub>1</sub>x + a<sub>2</sub>x<sup>2</su...

Solution