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Home / Doubts and Solutions/JEE/Mathematics

Ques 36

Asked by chandanbr6004 30th November 2017, 9:47 PM
Answered by Expert
Answer:
begin mathsize 16px style open parentheses straight x plus 1 close parentheses to the power of negative 1 end exponent cross times open parentheses straight x plus 2 close parentheses to the power of negative 1 end exponent open parentheses straight x plus 1 close parentheses to the power of negative 1 end exponent cross times open parentheses straight x over 2 plus 1 close parentheses to the power of negative 1 end exponent cross times 1 half now space coeff space of space straight x to the power of straight r space in space left parenthesis 1 plus straight x right parenthesis to the power of negative straight n end exponent space is space given space by space open parentheses negative 1 close parentheses to the power of straight r space cross times space straight C presuperscript straight n plus straight r minus 1 end presuperscript subscript straight r now space for space straight x to the power of 4 space we space need space corresponding space tems space from space both space the space expansions space ie. open parentheses space straight x to the power of 0 space from space open parentheses straight x plus 1 close parentheses to the power of negative 1 end exponent space close parentheses cross times open parentheses space straight x to the power of 4 space from space open parentheses straight x over 2 plus 1 close parentheses to the power of negative 1 end exponent space close parentheses open parentheses space straight x to the power of 1 space from space open parentheses straight x plus 1 close parentheses to the power of negative 1 end exponent space close parentheses cross times open parentheses space straight x cubed space from space open parentheses straight x over 2 plus 1 close parentheses to the power of negative 1 end exponent space space close parentheses open parentheses space straight x squared space from space open parentheses straight x plus 1 close parentheses to the power of negative 1 end exponent space close parentheses cross times open parentheses space straight x squared space from space open parentheses straight x over 2 plus 1 close parentheses to the power of negative 1 end exponent space space close parentheses open parentheses space straight x cubed space from space open parentheses straight x plus 1 close parentheses to the power of negative 1 end exponent space close parentheses cross times open parentheses space straight x to the power of 1 space from space open parentheses straight x over 2 plus 1 close parentheses to the power of negative 1 end exponent space close parentheses open parentheses space straight x to the power of 4 space from space open parentheses straight x plus 1 close parentheses to the power of negative 1 end exponent space close parentheses cross times open parentheses space straight x to the power of 0 space from space open parentheses straight x over 2 plus 1 close parentheses to the power of negative 1 end exponent space space close parentheses so space coeff space are open square brackets open parentheses negative 1 close parentheses to the power of 0 space cross times space straight C presuperscript 1 plus 0 minus 1 end presuperscript subscript 0 close square brackets cross times open square brackets open parentheses negative 1 close parentheses to the power of 4 space cross times space straight C presuperscript 1 plus 4 minus 1 end presuperscript subscript 4 cross times open parentheses 1 half close parentheses to the power of 4 close square brackets plus open square brackets open parentheses negative 1 close parentheses to the power of 1 space cross times space straight C presuperscript 1 plus 1 minus 1 end presuperscript subscript 1 close square brackets cross times open square brackets open parentheses negative 1 close parentheses cubed space cross times space straight C presuperscript 1 plus 3 minus 1 end presuperscript subscript 3 cross times open parentheses 1 half close parentheses cubed close square brackets plus open square brackets open parentheses negative 1 close parentheses squared space cross times space straight C presuperscript 1 plus 2 minus 1 end presuperscript subscript 2 close square brackets cross times open square brackets open parentheses negative 1 close parentheses to the power of 4 space cross times space straight C presuperscript 1 plus 2 minus 1 end presuperscript subscript 2 cross times open parentheses 1 half close parentheses squared close square brackets plus open square brackets open parentheses negative 1 close parentheses cubed space cross times space straight C presuperscript 1 plus 3 minus 1 end presuperscript subscript 3 close square brackets cross times open square brackets open parentheses negative 1 close parentheses to the power of 1 space cross times space straight C presuperscript 1 plus 1 minus 1 end presuperscript subscript 4 cross times open parentheses 1 half close parentheses to the power of 1 close square brackets plus open square brackets open parentheses negative 1 close parentheses to the power of 4 space cross times space straight C presuperscript 1 plus 4 minus 1 end presuperscript subscript 4 close square brackets cross times open square brackets open parentheses negative 1 close parentheses to the power of 0 space cross times space straight C presuperscript 1 plus 0 minus 1 end presuperscript subscript 0 cross times open parentheses 1 half close parentheses to the power of 0 close square brackets equals open parentheses 1 over 16 plus 1 over 8 plus 1 fourth plus 1 half plus 1 close parentheses 1 half equals 31 over 32 end style
Answered by Expert 1st December 2017, 7:00 PM
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