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Let $\mathrm{S_n=\sum_{r=1}^n r !}$ . If $\mathrm{T_n=S_n-7\left[\frac{S_n}{7}\right]}$ , where $\mathrm{\left [ x \right ]}$ denotes greatest integer $\mathrm{\leq x}$ , then $\mathrm{T_{100}}$ is equal to
Option: 1
7

Option: 2
5

Option: 3
11

Option: 4
none of these

Answers (1)

best_answer

Use the fact that $\mathrm{r!}$ is divisible by 7 whenever $\mathrm{r \geq 7}$ .

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