A Study of Sequences and Series with Applications to Financial Models

Mathematics — 2025, Undergraduate

This study investigated the convergence of sequences and series and applied the results to financial models involving compounding and annuities. Theoretical tests for convergence were applied to representative series, and convergent cases were used to compute limiting values relevant to finance. The findings revealed that convergence tests identified behaviour reliably, while geometric-series results underpinned accurate valuation formulas. The study observed that divergence of series corresponded to unbounded model behaviour. It recommends explicit links between analysis and applied finance in instruction.

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