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 34504 by NECx last updated on 07/May/18

1−(1/2)+(1/3)−(1/5)+....  find the sum of the series

$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{5}}+.... \\ $$$${find}\:{the}\:{sum}\:{of}\:{the}\:{series} \\ $$

Commented by abdo mathsup 649 cc last updated on 07/May/18

the question  is not clear sir Necx...

$${the}\:{question}\:\:{is}\:{not}\:{clear}\:{sir}\:{Necx}... \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 07/May/18

log(1+t)=t−(t^2 /2)+(t^3 /3)−(t^4 /4)....  log(1−t)=−t−(t^2 /2)−(t^3 /3)−(t^4 /4)...  log2=1−(1/2)+(1/3)−(1/4)...  put t=i  log(1+i)=i−(i^2 /2)+(i^3 /3)−(i^4 /4)+(i^5 /5)...  pls recheck the probem pls

$${log}\left(\mathrm{1}+{t}\right)={t}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}+\frac{{t}^{\mathrm{3}} }{\mathrm{3}}−\frac{{t}^{\mathrm{4}} }{\mathrm{4}}.... \\ $$$${log}\left(\mathrm{1}−{t}\right)=−{t}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}−\frac{{t}^{\mathrm{3}} }{\mathrm{3}}−\frac{{t}^{\mathrm{4}} }{\mathrm{4}}... \\ $$$${log}\mathrm{2}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}... \\ $$$${put}\:{t}={i} \\ $$$${log}\left(\mathrm{1}+{i}\right)={i}−\frac{{i}^{\mathrm{2}} }{\mathrm{2}}+\frac{{i}^{\mathrm{3}} }{\mathrm{3}}−\frac{{i}^{\mathrm{4}} }{\mathrm{4}}+\frac{{i}^{\mathrm{5}} }{\mathrm{5}}... \\ $$$${pls}\:{recheck}\:{the}\:{probem}\:{pls} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com