Series

Learning objectives

Expand (a + b)ⁿ for a positive integer n using ⁿCᵣ = n!/(r!(n − r)!), and find a stated coefficient or the term independent of x, including in products such as (1 + 2x)(3 − x)⁶

Use uₙ = a + (n − 1)d and Sₙ = ½n[2a + (n − 1)d] to solve problems about arithmetic progressions

Use uₙ = arⁿ⁻¹ and Sₙ = a(1 − rⁿ)/(1 − r) to solve problems about geometric progressions

Decide whether a geometric progression converges using |r| < 1, and calculate its sum to infinity S∞ = a/(1 − r)

Solve problems that connect an arithmetic and a geometric progression by forming simultaneous equations in a, d and r