Lecture - 16 Chapter 9 Sequences & Series

Why sum to infinity in a Geometric Progression exists only for r less then 1? Derivation of rule for sum of infinite terms of a G.P.

Find the sum to infinity in each of the following Geometric Progression.

Question 1. \(1, \frac{1}{3}, \frac{1}{9}, …\)

Question 2. \(6, 1.2, 0.24, …\)

Question 3. \(5, \frac{20}{7}, \frac{80}{49}, …\)

Question 4. \(\frac{-3}{4}, \frac{3}{16}, \frac{-3}{64}, …\)

Question 5. Prove that \(3^{\frac{1}{2}}\times 3^{\frac{1}{4}}\times3^{\frac{1}{8}}… = 3\)

Question 6. Let \(x=1+a+a^2+…\) and \(y=1+b+b^2+…\), where \(|a|<1\) and \(|b|<1\). Prove that \(1+ab+a^2b^2+…= \frac{xy}{x+y-1}\)