COMEDK · Maths · 5. Sequences and Series
\(\sum_{k=1}^{20} k k\) !is equal to
- A 21 !
- B 20 ! + 1
- C \(21!-1\)
- D \(20!-1\)
Answer & Solution
Correct Answer
(C) \(21!-1\)
Step-by-step Solution
Detailed explanation
We have, \(\sum_{k=1}^{20} k k\) ! \(\begin{aligned} \sum_{k=1}^{20} k k! & =\sum_{k=1}^{20}(k+1-1) k!=\sum_{k=1}^{20}[(k+1) k!-k!] \\ & =\sum_{k=1}^{20}(k+1)!-\sum_{k=1}^{20} k
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