Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 820

\[\boxed{\mathbf{820}.}\]

\[e \approx 2 + \frac{1}{2} + \frac{1}{2 \bullet 3} + \frac{1}{2 \bullet 3 \bullet 4} +\]

\[+ \ldots + \frac{1}{2 \bullet 3 \bullet 4 \bullet \ldots \bullet n}\]

\[1)\ \ n = 7:\]

\[e \approx 2 + \frac{1}{2} + \frac{1}{6} + \frac{1}{24} + \frac{1}{120} +\]

\[+ \frac{1}{720} + \frac{1}{5040} \approx 2,7182539\]

\[2)\ \ n = 8:\]

\[e \approx 2 + \frac{1}{2} + \frac{1}{6} + \frac{1}{24} + \frac{1}{120} +\]

\[+ \frac{1}{720} + \frac{1}{5040} +\]

\[+ \frac{1}{40\ 320} \approx 2,7182788\]

\[3)\ Если\ n = 9,\ тогда:\]

\[e \approx 2 + \frac{1}{2} + \frac{1}{6} + \frac{1}{24} + \frac{1}{120} +\]

\[+ \frac{1}{720} + \frac{1}{5040} + \frac{1}{40\ 320} +\]

\[+ \frac{1}{362\ 880} \approx 2,7182815\]

\[4)\ n = 10:\]

\[e \approx 2 + \frac{1}{2} + \frac{1}{6} + \frac{1}{24} + \frac{1}{120} +\]

\[+ \frac{1}{720} + \ldots + \frac{1}{362\ 880} +\]

\[+ \frac{1}{3\ 628\ 800} \approx 2,7182819\]