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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.

SUPPLEMENTARY EXERCISE

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

Question 1. $1, \frac{1}{3}, \frac{1}{9}, …$

Question 2. $6, 1.2, 0.24, \dots$

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 $x=1+a+a^2+\dots$ and $y=1+b+b^2+\dots$ , where $|a|<1$ and $|b|<1$ . Prove that $1+ab+a^2b^2+…= \frac{xy}{x+y-1}$