Solution
= Solution
The annulus where $2^k<|x|^{-b}\le2^{k+1}$ has volume comparable to $2^{-kd/b}$ for large positive $k$. The <series> is therefore comparable to $\sum2^{k(1-d/b)}$, which converges exactly when $b<d$.
= Solution
The annulus where $2^k<|x|^{-b}\le2^{k+1}$ has volume comparable to $2^{-kd/b}$ for large positive $k$. The <series> is therefore comparable to $\sum2^{k(1-d/b)}$, which converges exactly when $b<d$.