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The 37 pages that link to Geometric series, each with the reason it gives.

• Power seriesBroader topic: It supplies a basic model of power-series convergence and algebra.

• Cauchy sequenceRelated: When the ratio has absolute value below one, its partial sums form a Cauchy sequence.

• Binomial theoremCompared with: It is another power expansion, but its terms follow a ratio pattern rather than binomial coefficients.

• Infinite seriesBroader topic: Its convergence and sum follow directly from a finite partial-sum formula.

• Partial sumBroader topic: Its finite partial sums follow a formula that exposes dependence on the ratio.

• Banach fixed-point theoremRelated: The contraction factor bounds the total remaining distance by a convergent geometric series.

• Laurent seriesRelated: Expanding Cauchy kernels as geometric series derives Laurent expansions.

• Radius of convergenceBroader topic: Its convergence condition makes the radius calculation transparent in a basic power-series example.

• Cyclotomic polynomialCompared with: The quotient (xⁿ − 1)/(x − 1) includes roots of several orders, unlike a single cyclotomic factor.

• Ratio testBroader topic: When successive term ratios approach a number below one, the series behaves like a convergent geometric series.

• Geometric distributionRelated: Summing geometric probabilities uses the same powers of the failure probability.

• Geometric progressionRelated: Adding progression terms produces a series with formulas governed by the same ratio.

• Convergence of a seriesBroader topic: Its convergence depends sharply on whether the ratio's absolute value is less than one.

• Divisor functionRelated: The prime-power formula for σₖ is a finite geometric series.

• Root testRelated: The root test compares term magnitudes with a geometric series.

• Cauchy productRelated: Multiplying two convergent geometric series gives a direct example of coefficient convolution.

• Comparison testRelated: Its known convergence threshold makes it a common comparison target.

• Exponential sumCompared with: Linear phases reduce to geometric series with explicit formulas.

• Convergent seriesBroader topic: Its convergence is decided exactly by whether the ratio's absolute value is below one.

• Perfect numberRelated: Summing the divisors of 2^(p−1)(2^p−1) produces the perfect-number identity.

• Abel's theorem (power series)Broader topic: Its partial sums supply the basic weight estimates behind common proofs.

• Annuity (mathematics)Related: Level-payment annuity formulas sum a geometric sequence of discounted payments.

• Jacobi triple productRelated: Expanding product factors uses geometric-series identities for powers of q.

• Cauchy condensation testRelated: Condensation converts many familiar power-law tests into geometric convergence questions.

• Repeating decimalRelated: A repeating decimal can be rewritten as a convergent geometric series to derive its fraction.

• Cauchy–Hadamard theoremRelated: Its exact convergence condition illustrates the threshold that the theorem generalizes.

• Euclid–Euler theoremRelated: Summing the divisors of 2^(p−1) gives the geometric series used in the forward direction.

• Legendre's formulaRelated: The powers p, p², p³ in the denominator form a geometric progression.

• Binomial seriesCompared with: At exponent \(-1\), the binomial series becomes the geometric series.

• Koch snowflakeRelated: The added areas form a convergent geometric series.

• Master theoremRelated: Work across recursion-tree levels often forms a geometric series.

• Weierstrass M-testBroader topic: Geometric majorants often make the M-test easy to apply.

• Equidistribution theoremRelated: For irrational α, its formula bounds the exponential sums used in the simplest proof.

• Pentagonal number theoremCompared with: The product uses infinitely many factors, each with a simple geometric-series reciprocal.

• Divergence of the sum of the reciprocals of the primesCompared with: Its simple convergence criterion contrasts with the subtler divergence of reciprocals restricted to primes.

• Goormaghtigh conjectureRelated: The repunit formula is the finite geometric-series identity applied to powers of a base.

• Nth-term testBroader topic: Its terms tend to zero exactly when the ratio’s magnitude is below one, yielding convergence.