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 21h comment when $\lim_{n\to\infty }\sum_{k=0}^n\binom{n}{k}x^k$ exist? your first approach is legitimate 2d comment what is the max possible combinations of 1 2 3 4 5 6 without repeating The number of ways to seat 6 people at the round table. By rotating each person you get the same seating. Hence $\frac{6!}{6}$. 2d comment How to calculate $\sum_{n=1}^{15}n(n!) = ?$ I'm practically devastated 2d comment How to calculate $\sum_{n=1}^{15}n(n!) = ?$ Use the property of factorial and cancel out the $S_n$ term 2d comment How to calculate $\sum_{n=1}^{15}n(n!) = ?$ $1+ 2! + \ldots n! + (n+1)! = \sum_{k=1}^{n} (k+1)! + 1$ 2d revised How to calculate $\sum_{n=1}^{15}n(n!) = ?$ edited body 2d comment How to calculate $\sum_{n=1}^{15}n(n!) = ?$ 1) Define $S_n$, 2) Add the next term on both sides, 3) Manipulate RHS with sm algebra, 4)Get the result 2d comment How to calculate $\sum_{n=1}^{15}n(n!) = ?$ explain what exactly? 2d answered Big O notation: ratio of two $O(\cdot)$'s is $O(\cdot)$ of the ratio? Feb 11 answered Given two real functions, $f$ and $g$, if $|f(x)|<1$ then \$|g(f(x))|