How can i find the radious of convergence and the interval of convergence for this series

The ratio or root tests are the usual go-to methods.

By the ratio test, the series will converge if



The limit reduces to



which means the series diverges everywhere except the point , where the series evaluates to 0. So because the series diverges, the interval of convergence is a single point, and so the radius of convergence is 0.

You have 2 sides that are 2 cms and you have 6 sides that are 1/2 cm and you have 4 sides that are 1 cm. the smallest sides are 1/2 the medium sized sides are 1 and the smallest are 1/2. so to find the perimeter you have to add them all up together so your answer will be 11 cm's