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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.

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