Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 184920 by Mastermind last updated on 13/Jan/23

$$\mathrm{Investigate}\mathrm{the}\mathrm{series}$$$$\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+...$$$$\mathrm{Does}\mathrm{it}\mathrm{Converges}\mathrm{or}\mathrm{Diverges}?$$

Answered by aba last updated on 14/Jan/23

$${\mathrm{S}}_{\mathrm{n}}=\underset{\mathrm{k}=1}{\sum ^{\mathrm{n}}}\frac{1}{\mathrm{k}(\mathrm{k}+1)}=\underset{\mathrm{k}=1}{\sum ^{\mathrm{n}}}(\frac{1}{\mathrm{k}}-\frac{1}{\mathrm{k}+1})=1-\frac{1}{\mathrm{n}+1}$$$$\text{Double subscripts: use braces to clarify}$$$$\mathrm{it}\mathrm{converges}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com