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← JEE Main 2016 · 10 Apr · Shift 1
MathematicsSingle correct+4 / -1Question 69 of 90

JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 69

The sum ∑r=110(r2+1)×(r!)\displaystyle\sum_{r=1}^{10}(r^2+1)\times(r!) is equal to :

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Answer and worked solution

Official answer: B

(r2+1)r!=r (r+1)!−(r−1) r!(r^2+1)r!=r\,(r+1)!-(r-1)\,r!, which telescopes: ∑r=110=10⋅11!\sum_{r=1}^{10}=10\cdot11!.

Topics:Special series sums
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