JEE MATHEMATICS MCQ: PERMUTATIONS

1 Easy

1 of 1

Application +4 | -1

Let

S_n=\sum\limits_{{r=1}}^n r!

. If

T_n=S_n-7\left[\frac{S_n}{7}\right]

, where

[x]

denotes greatest integer

\leq x

, then

T_{100}

is equal to

View answer and explanation

Correct option: B

The correct answer is 5 because for n >= 6, n! is divisible by 7, so the sum modulo 7 stabilizes, and we can calculate the sum of the first few terms modulo 7.

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