Ch 8 formally treats arithmetic and geometric progressions as sequences and series, introduces infinite GPs, relationship between AM and GM, and sum formulas for special series.
nth term: aₙ = a + (n−1)d. Sum: Sₙ = n/2[2a + (n−1)d]. Arithmetic mean of a and b: AM = (a+b)/2. n AMs between a and b: common difference = (b−a)/(n+1).
nth term: aₙ = arⁿ⁻¹. Sum: Sₙ = a(rⁿ−1)/(r−1) for r≠1. Infinite GP (|r|<1): S∞ = a/(1−r). Geometric mean of a and b: GM = √(ab).
Σk = n(n+1)/2. Σk² = n(n+1)(2n+1)/6. Σk³ = [n(n+1)/2]². AM ≥ GM for positive numbers (equality when all numbers are equal).
Download: https://ncert.nic.in/textbook/pdf/kemh108.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
An infinite GP converges (has a finite sum) only when |r| < 1 (common ratio between −1 and 1, exclusive). The sum is S∞ = a/(1−r). If |r| ≥ 1, the series diverges.
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