1st year uni student suggestion

[fervent junco]

1 $$\displaystyle{\mathcal{S} = \sum_{n=1}^{\infty}\frac{(-1)^{n-1}{\rm Ci}(na)}{n^2}}$$
where
0 \leq a \leq 2\pi.

2

calculate
$$\displaystyle{\sum_{n=1}^{+\infty}(-1)^n\left(\sum_{k=1}^{n}\frac{1}{2k-1}-\frac{\ln n}{2}-\frac{\gamma}{2}-\ln 2\right)}$$

[paper arch]

normalhuman1043
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

normalhuman1043

[fervent junco]

$$\int\limits_0^{\pi /4} {{x^2}\log \left( {\sin x} \right)dx$$

[paper arch]

normalhuman1043
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fervent junco]

Can first year University student solve this questions?