I am trying to solve the following inequality:
$2+\left(\frac{3}{2}\right)^{\frac{1}{2}}+\left(\frac{4}{3}\right)^{\frac{1}{3}}+\cdots+\left(\frac{n+1}{n}\right)^{\frac{1}{n}}
but I do not know how to do that. Please help me solve this inequality.