Question-197005

Question Number 197005 by MrGHK last updated on 06/Sep/23

Answered by MathematicalUser2357 last updated on 10/Sep/23

Σ_(n=0) ^∞ (((−1)^n )/n)(ψ(((an+2)/2))−ψ(((an+1)/2))) =((((−1)^0 )/0)(ψ(((a∙0+2)/2))−ψ(((a∙0+1)/2))))+∙∙∙ Division by 0 does not exist So this is divergent

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}\left(\psi\left(\frac{{an}+\mathrm{2}}{\mathrm{2}}\right)−\psi\left(\frac{{an}+\mathrm{1}}{\mathrm{2}}\right)\right) \\ $$$$=\left(\frac{\left(−\mathrm{1}\right)^{\mathrm{0}} }{\mathrm{0}}\left(\psi\left(\frac{\cancel{{a}\centerdot\mathrm{0}}+\mathrm{2}}{\mathrm{2}}\right)−\psi\left(\frac{\cancel{{a}\centerdot\mathrm{0}}+\mathrm{1}}{\mathrm{2}}\right)\right)\right)+\centerdot\centerdot\centerdot \\ $$$$\mathrm{Division}\:\mathrm{by}\:\mathrm{0}\:\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$$$\mathrm{So}\:\mathrm{this}\:\mathrm{is}\:\mathrm{divergent} \\ $$

Facebook Tweet Pin

Question-197005

Leave a Reply Cancel reply