Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 68611 by TawaTawa last updated on 14/Sep/19

Answered by mind is power last updated on 15/Sep/19

(1/(r^2 −4))=(1/(4(r−2)))−(1/(4(r+2)))  ⇒Σ_(r=3) ^(100) (1/(r^2 −4))=(1/4)Σ((1/(r−2))−(1/(r+2)))=(1/4)(1+(1/2)+(1/3)+(1/4)−(1/(99))−(1/(100))−(1/(101))−(1/(102)))  x=25(1+(1/2)+(1/3)+(1/4)−(1/(99))−(1/(100))−(1/(101))−(1/(102)))=51.088....  [x]=51

$$\frac{\mathrm{1}}{{r}^{\mathrm{2}} −\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{4}\left({r}−\mathrm{2}\right)}−\frac{\mathrm{1}}{\mathrm{4}\left({r}+\mathrm{2}\right)} \\ $$$$\Rightarrow\sum_{{r}=\mathrm{3}} ^{\mathrm{100}} \frac{\mathrm{1}}{{r}^{\mathrm{2}} −\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{4}}\Sigma\left(\frac{\mathrm{1}}{{r}−\mathrm{2}}−\frac{\mathrm{1}}{{r}+\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{99}}−\frac{\mathrm{1}}{\mathrm{100}}−\frac{\mathrm{1}}{\mathrm{101}}−\frac{\mathrm{1}}{\mathrm{102}}\right) \\ $$$${x}=\mathrm{25}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{99}}−\frac{\mathrm{1}}{\mathrm{100}}−\frac{\mathrm{1}}{\mathrm{101}}−\frac{\mathrm{1}}{\mathrm{102}}\right)=\mathrm{51}.\mathrm{088}.... \\ $$$$\left[{x}\right]=\mathrm{51} \\ $$

Commented by TawaTawa last updated on 17/Sep/19

God bless you sir

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com