test","extracted_subject":"MATH","extracted_chapter":"PROGRESSIONS","extracted_topic":"ARITHMETIC PROGRESSION","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1945.png?top_left_x=532&top_left_y=0&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31ebe5","slug":"31sup3sup-32sup3sup-50sup3sup--1","content":"31³ + 32³ + ………… + 50³ =","options":[{"_id":"68a9343a7f15af4716d353a5","text":"1409400","sequence":0,"isCorrect":true},{"_id":"68a9343a7f15af4716d353a6","text":"1409000","sequence":1,"isCorrect":false},{"_id":"68a9343a7f15af4716d353a7","text":"1408400","sequence":2,"isCorrect":false},{"_id":"68a9343a7f15af4716d353a8","text":"None","sequence":3,"isCorrect":false}],"correct_answer":"1409400","explanation":"Let \\(\\mathrm { S } _ { \\mathrm { n } } = 1 ^ { 3 } + 2 ^ { 3 } + \\ldots \\ldots + \\mathrm { n } ^ { 3 } = \\left[ \\frac { \\mathrm { n } ( \\mathrm { n } + 1 ) } { 2 } \\right] ^ { 2 }\\) \n\n31³ + 32³ + 33³ + ……. + 50³ = S₅₀ – S₃₀\n\n₌ \\(\\left( \\frac { 50 ( 50 + 1 ) } { 2 } \\right) ^ { 2 } - \\left( \\frac { 30 ( 30 + 1 ) } { 2 } \\right) ^ { 2 }\\)\n\n= 1625625 – 216225 = 1409400","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.075Z","__v":0,"vector_store_id":"6425a747-bd9a-4bc3-8740-6192bf0badcd","updated_at":"2024-08-30T21:49:38.075Z","isStarred":false},"params":{"questionSlug":"31sup3sup-32sup3sup-50sup3sup--1"}}]}]]

Question: 31<sup>3</sup> + 32<sup>3</sup> + ………… + 50<sup>3</sup> =...

Solution