Calculus Early Transcendentals / Ch.11 with correct answers

Sequences - a sequence is a function which takes the natural numbers as its domain Monotonic Sequence - A sequence that is increasing or decreasing Geometric Series Formula - Sn=a1(1-r^n)/(1-r) Telescopic Series - see pic Divergence Test - lim_(k-infinity) [a_k] doesn't equal zero, then the series Σa_k must diverge Harmonic Series - diverges Comparison Test - If 0≤An≤bn and if ∑bn converges, then ∑An converges Limit Comparison Test - if lim as n approaches ∞ of ratio of comparison series/general term is positive and finite, then series behaves like comparison series Alternating Series - ∑(from n=1 to infinity) (-1)^n-1 a{n}. Converges if 0a{n+1}a{n} and lim (as n approaches infinity) a{n}= 0 Alternating Series Test - lim as n approaches zero of general term = 0 and terms decrease, series converges Absolute Convergence Test - If the sum of |a[n]| converges, then the sum of a[n] converges. Ratio Test - lim as n approaches ∞ of ratio of (n+1) term/nth term 1, series converges Power Series