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Find the unit place digit in the expression given below.
1! + 2! + 3! + 4! + ....... + 20!
1! + 2! + 3! + 4! + ....... + 20!
- a)5
- b)0
- c)3
- d)9
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Find the unit place digit in the expression given below.1! + 2! + 3! +...
As, 5! = 1 × 2 × 3 × 4 × 5 will have 0 as its unit digit because of the presence of (2 × 5). Hence all factorials above it will have 0 as their unit digit
⇒ 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33
∴ Unit digit of (1! + 2! + 3! + 4! + ....... + 20!) = Unit digit of (1! + 2! + 3! + 4!) = 3
Most Upvoted Answer
Find the unit place digit in the expression given below.1! + 2! + 3! +...
Unit place digit in the expression 1! + 2! + 3! + 4! + ....... + 20!
1. Calculating factorials
- Factorial of a number n (denoted as n!) is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
- We need to calculate the factorials of numbers from 1 to 20 to find the unit place digit in the given expression.
2. Finding the unit place digit
- Starting with 1! = 1, then 2! = 2, 3! = 6, 4! = 24, 5! = 120, and so on.
- To find the unit place digit, we need to focus on the last digit of each factorial.
- For 1 to 9, the unit digit of factorial repeats every 4 numbers. For example, 1! = 1, 2! = 2, 3! = 6, 4! = 4, 5! = 0, 6! = 0, 7! = 0, 8! = 0, 9! = 0.
- Since the pattern repeats every 4 numbers, we can find a pattern for the unit digits of factorials from 1 to 20.
3. Calculating the unit digit pattern
- Unit digits for factorials from 1 to 20: 1, 2, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.
- As observed, after the 5th factorial, all subsequent factorials have 0 as the unit digit.
4. Conclusion
- Since the unit digit of 20! is 0, adding it to any other factorials will result in a unit digit of 0.
- Therefore, the unit place digit in the expression 1! + 2! + 3! + 4! + ....... + 20! is 0.
Therefore, the correct answer is option B) 0.
1. Calculating factorials
- Factorial of a number n (denoted as n!) is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
- We need to calculate the factorials of numbers from 1 to 20 to find the unit place digit in the given expression.
2. Finding the unit place digit
- Starting with 1! = 1, then 2! = 2, 3! = 6, 4! = 24, 5! = 120, and so on.
- To find the unit place digit, we need to focus on the last digit of each factorial.
- For 1 to 9, the unit digit of factorial repeats every 4 numbers. For example, 1! = 1, 2! = 2, 3! = 6, 4! = 4, 5! = 0, 6! = 0, 7! = 0, 8! = 0, 9! = 0.
- Since the pattern repeats every 4 numbers, we can find a pattern for the unit digits of factorials from 1 to 20.
3. Calculating the unit digit pattern
- Unit digits for factorials from 1 to 20: 1, 2, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.
- As observed, after the 5th factorial, all subsequent factorials have 0 as the unit digit.
4. Conclusion
- Since the unit digit of 20! is 0, adding it to any other factorials will result in a unit digit of 0.
- Therefore, the unit place digit in the expression 1! + 2! + 3! + 4! + ....... + 20! is 0.
Therefore, the correct answer is option B) 0.
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Find the unit place digit in the expression given below.1! + 2! + 3! + 4! + ....... + 20!a)5b)0c)3d)9Correct answer is option 'C'. Can you explain this answer?
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