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JEE Main202118 Mar 2021Evening ShiftMathematicsSequences and SeriesActual

If ∑ r = 1 10 r ! r 3 + 6 r 2 + 2 r + 5 = α 11 ! , then the value of α is equal to ___ .

Correct answer

0

Step-by-step solution

∑ r = 1 10 r ! r + 1 r + 2 r + 3 - 9 r + 1 + 8 = ∑ r = 1 10 ( r + 3 ) ! - ( r + 1 ) ! - 8 r + 1 ! - r ! = ( 13 ! + 12 ! - 2 ! - 3 ! ) - 8 ( 11 ! - 1 ) = ( 12 . 13 + 12 - 8 ) · 11 ! - 8 + 8 = ( 160 ) ( 11 ) ! Hence α = 160

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