Subject: Mathematics
Book: Maths Mastery
Arithmetic series Sₙ= (n/2)(a₁+aₙ) or (n/2)[2a₁+(n–1)d] sums n terms. Geometric series Sₙ= a₁(1–rⁿ)/(1–r) for r≠1. These standard results handle repeated adding or multiplying patterns. For example, if an arithmetic sequence is 5, 8, 11,... with n=6 terms, sum is (6/2)[2×5+(6–1)×3]=3[10+15]=75. Mastery helps with finances (loan amortization), repeated additions in budgeting, or analyzing growth in discrete steps. Summation formulas are cornerstones of advanced math, bridging simple patterns to deep combinatorial or calculus expansions.
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