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Evaluate the sum S = 1·1! + 2·2! + 3·3! + 4·4! + 5·5! + 6·6!, where…
Question
Evaluate the sum S = 1·1! + 2·2! + 3·3! + 4·4! + 5·5! + 6·6!, where n! denotes factorial. Give the exact integer value of S.
✓ Verified answer: 5039checked by our engine — not a guess
Step-by-step solution
Use the identity k·k! = (k+1)! - k!. Then the sum telescopes:
S = Σ_{k=1}^{6} [(k+1)! - k!] = 7! - 1! = 5040 - 1 = 5039.
Final answer5039
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