Summation upto 10 terms r=1

r/(4r^4+1)

summation upto 7 terms r=1

tan^2 {r(pi)}/16

hi .. !

        for the first question ,

                   ∑⁷_r=1 r/(4r⁴ +1)  , by expnding this we get

                        1/5 + 2/65 + 3/ 325 + … 10 / 40001 by looking this series we can understand that first and second terms only yield most significant value & rest of the terms almost negligible , so  the value we obtained is –

                0.230769231 or it is > 0.23 & less than 0.24

 for the second summation , anyway tan (nπ) , n= 1, 2, 3 … is ‘0’

    so the summation also ‘0’ for all ‘r’ .