Question

find the remainder when 1! + 2! +. +100 is divided by 15
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Answer 1

find sum to the factorial 100

S(n) = n×(n+1)÷2

S =100×101÷2

100

=5050

now divide 5050 by 15

remainder=10

Answer 2

3 is the answer.

Step-by-step explanation:

• First, simply enlarge a number of the beginning factorials.
• 1! = 1 x 1
• 2! = 2 x 1
• 3! = 3 x 2 x 1
• 4! = 4 x 3 x 2 x 1, and 5! = 5 x 4 x 3 x 2 x 1.
• So it's far surely seen that 5! is a multiple of 15 because it consists of five and three in its expansion, so if we divide five! via way of means of 15, the remainder can be zero.
• And  all the imminent factorials can be a multiple of 15, as
• 6! = 6 x 5!
• 7! = 7 x 6 x 5!
• .............
• So, the factorial with the intention to have an effect on the rest are,
• 1! + 2! + three! + four! = 1 + 2 + 6 + 24 = 33
• So, while 33 is split via way of means of 15 the rest is three.
• So, the solution has to be 3.

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