∑n=1∞n\sum_{n=1}^{\infty}{n}

asked by guest
on Mar 28, 2025 at 4:16 am



You asked:

Evaluate the expression: ∑n=1∞n\sum_{n = 1}^{\infty} {n}

MathBot Answer:

The infinite series ∑n=1∞n\displaystyle\sum_{n=1}^{\infty} n diverges.

We can use the p-series test to determine convergence of this series.

Given a series ∑n=k∞1np\displaystyle\sum_{n=k}^{\infty} \frac{1}{n^p} where pp is a positive real number and k>0k>0,
 •If p>1p > 1 the series converges.
 •If p≤1p \le 1 the series diverges.
an=np=−1−1≤1\begin{aligned}a_n &= n\\ p &=-1\\ -1 &\le 1\end{aligned}Therefore the series diverges.

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