Question

is this valid?

Answer 1

\[\frac{ .4 }{ \pi }\sum_{n=1}^{\infty} \frac{ 1 }{ n }\sin(\frac{ n*\pi }{ 5 })\cos(\frac{n*\pi*t}{2})=....\]

Answer 2

\[\frac{ .4 }{ \pi }\sum_{n=1}^{\infty} \frac{ 1 }{ n }\sin(\frac{ n*\pi }{ 5 })\sum_{n=1}^{\infty} \frac{ 1 }{ n }\cos(\frac{n*\pi*t}{2})\]

Answer 3

I don't think so,

\[\sum_{n=1}^\infty a_nb_n = a_1b_1 + a_2b_2+a_3b_3+\cdots\]\[\sum_{n=1}^\infty a_n\sum_{n=1}^\infty b_n = (a_1+a_2+a_3+\cdots)(b_1+b_2+b_3+\cdots)\]

Answer 4

Right? @optiquest

Answer 5

Yes