Real Analysis - Convergence [closed]
Convergence testing -
Q. How can we prove that Σ[1/(n^c)] is convergent? (where n ε N, c = constant, c > 1).
Tried proving using Cauchy's Fundamental theorem but could not reach to the solution.
Solution 1:
The function $f(x)=\frac{1}{x^c}$ is positive and decreasing on $[1,\infty)$. Hence, by the integral test (proof is easy to understand), the series converges for $c>1$.