How does the calculator validate arithmetic partial sums?

We require integer indices with N ≥ n0. When d = 0 the tool reduces S to k × a1 and surfaces that branch in the step log.

What happens if the geometric infinite series does not converge?

If |r| ≥ 1 the infinite sum diverges. The calculator stops, explains the convergence condition, and keeps the previous result unchanged.

Sequences & Series (Arithmetic / Geometric)

What you can do

Arithmetic (AS) and geometric (GS) nth terms, interval sums, solving for n or k, and two-term inference
Generate copy-ready tables of t_n and cumulative S_n for any interval
Display every substitution in a dedicated “How it’s calculated” column for classroom-friendly steps
Share URLs, copy LaTeX, toggle teacher notes, and load comments on demand

Mode

Result

How it's calculated

Teacher notes

FAQ

How are logarithms handled when solving geometric terms?

For r > 0 we solve n = n0 + log(T/a1) / log(r). For r < 0 we additionally enforce |r|^k = |T/a1| and (-1)^k = sign(T/a1); otherwise the tool reports that the parity constraint fails.

Can I export the generated table?

Yes. After computing, click “Copy as CSV” to push a tidy n,t_n,S_n table to your clipboard, ready for spreadsheets or LMS uploads.

Sequences & Series Calculator

What you can do

Mode

Result

How it's calculated

Teacher notes

FAQ

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