Question:

The ten's digit in 1!+4!+7!+10!+12!+13!+15!+16!+17!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!10 ! and above factorials will be zero- zero. ∴1!+4!+7!+10!+12!+13!+15!+16!+17!\therefore 1 !+4 !+7 !+10 !+12 !+13 !+15 !+16 !+17 ! =1+24+5040+10!+12!+13!+15!+16!+17!=1+24+5040+10 !+12 !+13 !+15 !+16 !+17 ! =5065+10!+12!+13!+15!+16!+17!=5065+10 !+12 !+13 !+15 !+16 !+17 ! In this series, the digit in the ten place is 66 which is divisible by 3!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.