WBJEE · Maths · Sequences and Series
The sum \(1 \times 1!+2 \times 2!+\ldots+50 \times 50\) ! equals
- A \(51 !\)
- B \(51 !-1\)
- C \(51 !+1\)
- D \(2 \times 51 !\)
Answer & Solution
Correct Answer
(B) \(51 !-1\)
Step-by-step Solution
Detailed explanation
\(1 \times 1!+2 \times 2!+\ldots+50 \times 50!\) \(=(2-1) 1!+(3-1) 2!+(4-1) 3 !\) \(+\ldots+(51-1) 50!\) \(=(2 !-1!)+(3 !-2!)+(4 !-3 !)+(51!-50!)\) \(+\ldots+(511-501)\) \(=511-11=511-1\)
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