If a, b, and c are positive real numbers and a² + b² + c² = 3, what is the minimum value of the expression [1/(1+ab)] + [1/(1+bc)] + [1+(1+ac )]?
Usage: A² + B² + C² ≥ AB+AC+BC
Answer: 3/2
How do I know whether or not the series
$$ \sum_{n=1}^\infty sin(\frac{n\pi}{2})sin(nx)$$
converges pointwise for all real x or not?
By the way am I right in thinking that converging pointwise for all real x means whatever x i plug into the series it converges to some finite value?
I was...