JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\sum_{r=1}^{10} r !\left( r ^{3}+6 r ^{2}+2 r +5\right)=\alpha(11 !),\) then the value of \(\alpha\) is equal to ...... .
- A \(180\)
- B \(148\)
- C \(160\)
- D \(176\)
Answer & Solution
Correct Answer
(C) \(160\)
Step-by-step Solution
Detailed explanation
\(\sum_{ r =1}^{10} r !\{( r +1)( r +2)( r +3)-9( r +1)+8\}\) \(=\sum_{ r =1}^{10}[\{( r +3) !-( r +1) !\}-8\{( r +1) !- r !\}]\) \(=(13 !+12 !-2 !-3 !)-8(11 !-1)\) \(=(12.13+12-8) \cdot 11 !-8+8\) \(=(160)(11) !\) Hence \(\alpha=160\)
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