Determine whether the following series converge or diverge:
a) $\sum_{n=1}^{\infty} \frac{12}{n^{12}}$
b) $\sum_{n=1}^{\infty} \frac{\sqrt{n}}{12 n}$
A)(a)converges and (b)diverges
B)(a)diverges and (b)converges
C)both series diverge
D)both series converge

Question

Determine whether the following series converge or diverge: 
a) $\sum_{n=1}^{\infty} \frac{12}{n^{12}}$ 
b) $\sum_{n=1}^{\infty} \frac{\sqrt{n}}{12 n}$
A)(a)converges and (b)diverges
B)(a)diverges and (b)converges
C)both series diverge
D)both series converge

Quizplus · Accepted Answer

a) This series is a p-series with $p = 12$, which converges because $p > 1$. b) This series simplifies to $\sum_{n=1}^{\infty} \frac{1}{12\sqrt{n}}$, which is a p-series with $p = 1/2$, and diverges because $p \leq 1$.

Determine Whether the Following Series Converge or Diverge: A) ∑n=1∞12n12\sum_{n=1}^{\infty} \frac{12}{n^{12}}∑n=1∞​n1212​

Determine Whether the Following Series Converge or Diverge:
A) $\sum_{n=1}^{\infty} \frac{12}{n^{12}}$