Question Number 216886 by Engr_Jidda last updated on 23/Feb/25
$${Evaluate}\:\frac{\underset{{k}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\int_{\mathrm{0}} ^{{k}} \left(\mathrm{4}{u}+\mathrm{1}\right){du}\right)}{\mathrm{5}^{\mathrm{2}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left(\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{2}}{{m}^{\mathrm{2}} +\mathrm{2}{m}}\right)^{{n}−\mathrm{1}} }\int_{{sin}^{−\mathrm{1}} \left(\frac{−\sqrt{\mathrm{2}}}{\mathrm{2}}\right)} ^{\frac{\pi}{\mathrm{2}}{cos}\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}−{sec}\theta{sin}\theta}{\frac{{tan}\theta+{cot}\theta}{\varrho^{\theta} −\varrho^{\pi{i}} }}\right){d}\theta \\ $$
Commented by MathematicalUser2357 last updated on 24/Feb/25
$${we}\:{can}\:{use}\:{the}\:{formula}\:{to}\:{clean}\:{this}\:{gibberish} \\ $$