2! + 4! + 6! + 8! + 10! +………….+100! When divided by 5, will give remainder.2301

The given series is a factorial series with an increment of 2.

The factorial of any number greater than or equal to 5 is always divisible by 5. This is because the factorial of a number is the product of all positive integers less than or equal to that number, and for numbers greater than or equal to 5, one of those integers will be 5, making the factorial divisible by 5.

So, from 5! onwards, all terms in the series are divisible by 5.

Therefore, we only need to consider the first two terms to find the remainder when divided by 5.

2! = 2 4! = 24

Adding these gives 2 + 24 = 26

So, when 26 is divided by 5, the remainder is 1.

Therefore, the remainder when the given series is divided by 5 is 1.