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AP EAMCET201823 Apr 2018Morning ShiftMathematicsBinomial TheoremActual

1 4 - 5 4 8 + 5 7 4 8 12 - =

Options

  1. A3 3 -2 5 9 3
  2. B2 3 -3 2 9 3
  3. C3 3 -2 2 9 3
  4. D2 3 -3 5 9 3

Correct answer

C. 3 3 -2 2 9 3

Step-by-step solution

aligned & Let S= 1 4 - 5 4 8 + 5 7 4 8 12 - & = 1 3 ( 3 4 - 3 5 4 8 + 3 5 7 4 8 12 - ) aligned Now, we know that (1+x)^ -n =1-n x+ n(n+1) 2 ! x^2 aligned & Put n= 3 2 and n= 1 2 & aligned 3 2 1 2 & - 3 2 5 2 2 ! ( 1 2 )^2+ = & 1- (1+ 1 2 )^ -3 / 2 =1- ( 3 2 )^ -3 / 2 & =1- ( 2 3 )^ 3 / 2 =1- 2 2 3 3 = 3 3 -2 2 3 3 aligned aligned put in Eq. (i), we get S= 1 3 ( 3 3 -2 2 3 3 ) S= 3 3 -2 2 9 3

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