Hi! Problem: $\displaystyle \sum_{k=1}^{\infty} (\sqrt[k]{k}-1) $ , convergent or divergent? Thx
Follow Math Help Forum on Facebook and Google+
Use $\displaystyle x>\ln(1+x)$ for $\displaystyle x>0$ with $\displaystyle x=\root k\of k-1$. Then $\displaystyle \root k\of k-1>\ln(\root k\of k)=\frac{\ln k}k$. By comparison with $\displaystyle \sum\frac1k$ the series diverges.
That is clever!
View Tag Cloud