Convergence and divergence of normal infinite series

Intros
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Lessons
  1. Overview of Converging and Diverging Series
Examples
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Lessons
  1. Converging and Diverging Series with the formula of partial sums

    You are given the general formula of partial sums for the following series. Determine whether the series converges or diverges.
    1. ∑n=1Nan=N2+2N+3N+6 \sum_{n=1}^{N}a_n=\frac{N^2+2N+3}{N+6}
    2. ∑n=1Nan=N2+6N+2N2+4 \sum_{n=1}^{N}a_n=\frac{N^2+6N+2}{N^2+4}
    3. ∑n=1Nan=N+5N2+1 \sum_{n=1}^{N}a_n=\frac{N+5}{N^2+1}
  2. Converging and Diverging Series without the formula of partial sums

    Determine whether the following series converges or diverges.
    1. ∑n=1∞n \sum_{n=1}^{\infty}n
    2. ∑n=1∞n3 \sum_{n=1}^{\infty}n^3
    3. 2+4+6+8+ ...