The correct option is B 11! 1Given, ∑ _k=1^10kk! a_k=kk! a_1=1· 1!=1 a_2=2· 2!=4 Similarly, a_3=18 a_4=96 a_5=600 a_6=432 ...

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Factorial

∑ k=1 10 k.k!...

Question

$\sum_{k = 1}^{10} k . k! =$

10!

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11!

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10!+1

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11!-1

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Solution

The correct option is B 11!-1
Given,

$\sum_{k = 1}^{10} k k!$

$a_{k} = k k!$

$a_{1} = 1 \cdot 1! = 1$

$a_{2} = 2 \cdot 2! = 4$

Similarly,

$a_{3} = 18$

$a_{4} = 96$

$a_{5} = 600$

$a_{6} = 4320$

$a_{7} = 35280$

$a_{8} = 322560$

$a_{9} = 3265920$

$a_{10} = 36288000$

$= 1 + 4 + 18 + 96 + 600 + 4320 + 35280 + 322560 + 3265920 + 36288000$

$= 39916799$

$= 11! - 1$

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