test","extracted_subject":"MATH","extracted_chapter":"PROGRESSIONS","extracted_topic":"nth TERM OF SPECIAL SERIES, SUM TO n TERMS AND INFINITE NUMBER OF TERMS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1964.png?top_left_x=0&top_left_y=1003&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31eeb5","slug":"if-1-x-1-xsup2sup-1-xsup4sup1-xsup128sup-media-v2-","content":"If (1 + x) (1 + x²) (1 + x⁴)……(1 + x¹²⁸) = ![](https://cdn.pureessence.tech/canvas_247.png?top_left_x=300&top_left_y=1740&width=264&height=300) then n is –","options":[{"_id":"68a44bd97f15af4716cb9076","text":"225","sequence":0,"isCorrect":false},{"_id":"68a44bd97f15af4716cb9077","text":"255","sequence":1,"isCorrect":true},{"_id":"68a44bd97f15af4716cb9078","text":"60","sequence":2,"isCorrect":false},{"_id":"68a44bd97f15af4716cb9079","text":"127","sequence":3,"isCorrect":false}],"correct_answer":"255","explanation":"(1 + x) (1 + x²) (1 + x³)…..(1 + x¹²⁸)\n\n= 1 + x + x² + ….+ xⁿ\n\ñ (1 – x) {(1 + x) (1 + x²) (1 + x³)}……(1 + x¹²⁸)\n\ñ (1 – x²⁵⁶) = (1 – x^{n + 1})\n\ñ n + 1 = 256\n\nn = 225.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.254Z","__v":0,"vector_store_id":"37d55112-bf98-41b1-aa9a-6de6d8de211b","updated_at":"2024-08-30T21:49:38.254Z","isStarred":false},"params":{"questionSlug":"if-1-x-1-xsup2sup-1-xsup4sup1-xsup128sup-media-v2-"}}]}]]

Question: If (1 + x) (1 + x<sup>2</sup>) (1 + x<sup>4</sup>)……(1 + x<sup>128</sup>) = ![](https://cdn.pureesse...

Solution