Sequence of partial sums

Sequence of Partial Sums Given a sequence

, the partial sums form a new sequence

defined by

The left graph shows the terms

of the sequence. The right graph shows the corresponding partial sums

. Things to try:

Adjust the slider n to see how the partial sums accumulate term by term.

Edit the Sequence formula input box to explore different sequences.

Example: 2*(1/3)^n — a convergent geometric series; watch

approach

Example: (-1)^(n+1)/n — the alternating harmonic series; converges to

Example: 1/n — the harmonic series; does

converge?

Example: 1/n^2 — converges to

Notice how a sequence can have terms approaching

yet still diverge.

Nuevos recursos