Recent content by Tsss

The fact that (a^b)^c=a^{bc} is not right with complex numbers. As a matter of fact, let z a complex number, e^z=e^{\frac{2i\pi z}{2i\pi}}=(e^{2i\pi})^{\frac{z}{2i\pi}}=1^{\frac{z}{2i\pi}}=1 there is a problem.

X_n=\sum_{k=1}^n 1 Y_n=\sum_{k=1}^n -1

n\ln(1 - \frac{1}{n^2})\sim-\frac{n}{n^2}=-\frac{1}{n}\rightarrow 0 So, (1 - \frac{1}{n^2})^{n}-1=e^{n\ln(1 - \frac{1}{n^2} )}-1\sim-\frac{1}{n} Now, you can conclude ;).

What does w<=2 mean for a complex number ?

I would like to add something about sequences and subsequences. That's right that you can't conclude about the convergence of a sequence only working on his subsequences...in the most cases. Indeed, if two subsequences has two different limits, then the sequence has no limit (because if a...