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Home / Doubts and Solutions/JEE/Mathematics

1.3.2^2+2.4.3^2+3.5.4^2+....=?

Asked by jaychandran1967 7th June 2018, 12:59 PM
Answered by Expert
Answer:
begin mathsize 16px style Given space series space can space be space written space as straight T subscript straight n equals straight n left parenthesis straight n plus 2 right parenthesis left parenthesis straight n plus 1 right parenthesis squared space space space space space equals straight n to the power of 4 space plus space 4 straight n cubed space plus space 5 straight n squared space plus space 2 straight n Sum space of space straight n space terms space will space be straight S subscript straight n space equals space stack sum straight n to the power of 4 with straight n below space plus space 4 stack sum straight n cubed with straight n below space plus space stack 5 sum straight n squared with straight n below space plus space 2 stack sum straight n with straight n below space space space space space space equals stack sum open parentheses straight n squared close parentheses squared with straight n below space plus space 4 open parentheses straight n open parentheses fraction numerator straight n plus 1 over denominator 2 end fraction close parentheses close parentheses squared space plus space 5 fraction numerator straight n open parentheses straight n plus 1 close parentheses open parentheses 2 straight n plus 1 close parentheses over denominator 6 end fraction plus 2 cross times fraction numerator straight n open parentheses straight n plus 1 close parentheses over denominator 2 end fraction space space space space space space space equals open square brackets fraction numerator straight n open parentheses straight n plus 1 close parentheses open parentheses 2 straight n plus 1 close parentheses over denominator 6 end fraction close square brackets squared space plus space 4 open parentheses straight n open parentheses fraction numerator straight n plus 1 over denominator 2 end fraction close parentheses close parentheses cubed plus 5 fraction numerator straight n open parentheses straight n plus 1 close parentheses open parentheses 2 straight n plus 1 close parentheses over denominator 6 end fraction plus straight n open parentheses straight n plus 1 close parentheses end style
Answered by Expert 8th June 2018, 12:27 PM
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