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The ten's digit in $1! + 4!+ 7! + 10!+12! + 13! + 15! +16! + 17!$ is divisible by
The ten's digit in $1! + 4!+ 7! + 10!+12! + 13! + 15! +16! + 17!$ is divisible by
Updated On: Aug 15, 2022
- 4
- 3!
- 5
- 7
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The Correct Option is B
Solution and Explanation
As we know the last two digits of $10 !$ and above factorials will be zero- zero.
$\therefore 1 !+4 !+7 !+10 !+12 !+13 !+15 !+16 !+17 !$
$=1+24+5040+10 !+12 !+13 !+15 !+16 !+17 !$
$=5065+10 !+12 !+13 !+15 !+16 !+17 !$
In this series, the digit in the ten place is $6$ which is divisible by $3 !$
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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.
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