Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 205574 by Red1ight last updated on 24/Mar/24

$$S=\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}...$$$$S=?$$

Commented by Frix last updated on 25/Mar/24

$$S=\frac{1}{\mathrm{e}}$$

Answered by mathzup last updated on 25/Mar/24

$$S=\sum _{n=2}^{\mathrm{\infty }}\frac{{(-1)}^n}{n!}=\sum _{n=0}^{\mathrm{\infty }}\frac{{(-1)}^n}{n!}-1-(-1)$$$$=\frac{1}{e}(\sum _{n=0}^{\mathrm{\infty }}\frac{x^n}{n!}=e^x)$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com