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Sir pls solve the following.
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Asked by rsudipto | 22 Dec, 2018, 08:19: PM
answered-by-expert Expert Answer
begin mathsize 16px style open parentheses 1 plus x plus x squared plus x cubed close parentheses to the power of n space equals space sum from r equals 0 to 3 n of b subscript r x to the power of r space space.................. left parenthesis 1 right parenthesis l e t space u s space s u b s t i t u t e space space x space equals space 1 space i n space e q n. left parenthesis 1 right parenthesis comma space space t h e n space w e space h a v e space space space 4 to the power of n space equals space space sum from r equals 0 to 3 n of b subscript r space space equals space k space space............... left parenthesis 2 right parenthesis d i f f e r e n t i a t e space e q n. left parenthesis 1 right parenthesis comma space t h e n space w e space h a v e space space space space n open parentheses 1 space plus space x space plus space x squared space plus space x cubed close parentheses to the power of n minus 1 end exponent space open parentheses 3 x squared space plus space 2 x space plus space 1 close parentheses space equals space space stack sum r space with r equals 0 below and 3 n on top b subscript r x to the power of r minus 1 end exponent space............... left parenthesis 3 right parenthesis l e t space u s space s u b s t i t u t e space space x space equals space 1 space i n space e q n. left parenthesis 3 right parenthesis comma space space t h e n space w e space h a v e space space space n cross times 4 to the power of n minus 1 end exponent cross times 6 space equals space space stack sum r with r equals 0 below and 3 n on top b subscript r space........... left parenthesis 4 right parenthesis s u b s t i t u t i n g space f o r space 4 to the power of n space f r o m space e q n. left parenthesis 2 right parenthesis comma space w e space r e w r i t e space e q n. left parenthesis 4 right parenthesis space a s comma space space space stack sum r with r equals 0 below and 3 n on top b subscript r space space equals space fraction numerator n cross times k cross times 6 over denominator 4 end fraction space equals space 3 over 2 n k end style
Answered by Thiyagarajan K | 01 Jan, 2019, 09:50: PM

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