Question
Download Solution PDFFind the unit digit in 1! + 2! + 3! + 4! + …………… + 50!
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFComputing the factorials,
⇒ 1! = 1
⇒ 2! = 1 × 2 = 2
⇒ 3! = 1 × 2 × 3 = 6
⇒ 4! = 1 × 2 × 3 × 4 = 24
⇒ 5! = 1 × 2 × 3 × 4 × 5 = 120
As we can notice that the unit digit of 5! Is 0, hence, the unit digit of 6!, 7!, …, 50! will be zero
Unit's digit of (1! + 2! + 3! + 4! + …………… + 50!)
⇒ Unit's digit of (1! + 2! + 3! + 4!)
⇒ Unit's digit of (1 + 2 + 6 + 24)
∴ Unit's digit of (33) = 3
Alternate Method 1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
∴ Unit digit = 1+ 2+ 6 + 4 + 0 = 13 = 3
Last updated on May 28, 2025
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