Question:
The remainder obtained when \(1!+2!+3!+.....+11!\) is divided by 12 is
The remainder obtained when \(1!+2!+3!+.....+11!\) is divided by 12 is
Updated On: Apr 26, 2024
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The Correct Option is A
Solution and Explanation
The correct answer is A:9
\(1!+2!+3!+4!+......+11!\)
\(=(1!+2!+3!)+(4!+5!+.....+11!)\)
\(=(1+2+6)+(4!+5!+......+11!)\)
\(=9+(4!+6!+.....+11!)\)
\(4!,5!........11!\) are divisible by 12
So when you will divide given expression by 12 the remainder will be 9.
\(1!+2!+3!+4!+......+11!\)
\(=(1!+2!+3!)+(4!+5!+.....+11!)\)
\(=(1+2+6)+(4!+5!+......+11!)\)
\(=9+(4!+6!+.....+11!)\)
\(4!,5!........11!\) are divisible by 12
So when you will divide given expression by 12 the remainder will be 9.
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Concepts Used:
Binomial Theorem
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
- The number of coefficients in the binomial expansion of (x + y)n is equal to (n + 1).
- There are (n+1) terms in the expansion of (x+y)n.
- The first and the last terms are xn and yn respectively.
- From the beginning of the expansion, the powers of x, decrease from n up to 0, and the powers of a, increase from 0 up to n.
- The binomial coefficients in the expansion are arranged in an array, which is called Pascal's triangle. This pattern developed is summed up by the binomial theorem formula.