Evaluate-k-1-10-0-k-4u-1-du-5-2-n-1-1-2-n-2-2-m-2-2m-n-1-sin-1-2-2-pi-2-cos-pi-2-1-sec-sin-tan-cot-pii-d-

Question Number 216886 by Engr_Jidda last updated on 23/Feb/25

E v a l u a t e \frac{\underset{k = 1}{\sum^{10}} (\int_{0}^{k} (4 u + 1) d u)}{5^{2} \underset{n = 1}{\sum^{\infty}} \frac{1}{2} {(\underset{n = 2}{\sum^{\infty}} \frac{2}{m^{2} + 2 m})}^{n - 1}} \int_{{s i n}^{- 1} (\frac{- \sqrt{2}}{2})}^{\frac{π}{2} c o s \frac{π}{2}} (\frac{1 - s e c θ s i n θ}{\frac{t a n θ + c o t θ}{ϱ^{θ} - ϱ^{π i}}}) d θ

Commented by MathematicalUser2357 last updated on 24/Feb/25

w e c a n u s e t h e f o r m u l a t o c l e a n t h i s g i b b e r i s h