- Home
- Standard 11
- Mathematics
7.Binomial Theorem
hard
यदि $\sum_{ r =1}^{10} r !\left( r ^{3}+6 r ^{2}+2 r +5\right)=\alpha(11 !)$ है, तो $\alpha$ का मान बराबर है ............ |
A
$180$
B
$148$
C
$160$
D
$176$
(JEE MAIN-2021)
Solution
$\sum_{ r =1}^{10} r !\{( r +1)( r +2)( r +3)-9( r +1)+8\}$
$=\sum_{ r =1}^{10}[\{( r +3) !-( r +1) !\}-8\{( r +1) !- r !\}]$
$=(13 !+12 !-2 !-3 !)-8(11 !-1)$
$=(12.13+12-8) \cdot 11 !-8+8$
$=(160)(11) !$
Hence $\alpha=160$
Standard 11
Mathematics