CalcRef

Printable sheets · 18 rows · portrait

Sequences & Series formula sheet

All 18 Sequences & Series formulas in CalcRef on one printable page, each with its conditions. Convergence tests, power series, Taylor and Maclaurin series.

Sequences & Series formula sheet

18 rows · CalcRef · sample of the first 6 rows

Sequences & Series
FormulaStatementConditions
Sequence Convergencelim⁡n→∞an=L⇒{an} converges to L\lim_{n \to \infty} a_n = L \Rightarrow \{a_n\} \text{ converges to } Lno restriction stated
Geometric Sequencean=a1⋅rn−1a_n = a_1 \cdot r^{n-1}no restriction stated
Arithmetic Sequencean=a1+(n−1)da_n = a_1 + (n-1)dno restriction stated
Series (Partial Sums)∑n=1∞an=lim⁡N→∞∑n=1Nan=lim⁡N→∞SN\sum_{n=1}^{\infty} a_n = \lim_{N \to \infty} \sum_{n=1}^{N} a_n = \lim_{N \to \infty} S_Nno restriction stated
Geometric Series∑n=0∞arn=a1−rif ∣r∣<1\sum_{n=0}^{\infty} ar^n = \frac{a}{1-r} \quad \text{if } |r| < 1no restriction stated
p-Series∑n=1∞1np converges if p>1, diverges if p≤1\sum_{n=1}^{\infty} \frac{1}{n^p} \text{ converges if } p > 1 \text{, diverges if } p \leq 1no restriction stated

The 18 Sequences & Series formulas in the CalcRef library, every one of them free to read at /topics/sequences-series.

CalcRef is an educational reference. Check every statement on this sheet against your own course notes, textbook or exam formula policy before relying on it in graded work.

Every formula on this sheet is also free on its own page — browse the full reference. Premium pays for the sheet, not the mathematics.

CalcRef is an educational reference. Verify formulas for exams, engineering work, or professional use.