Class 11 Lecture 16 Sequences and Series

“The Three ‘C’s’ Of Leadership Are Consideration, Caring, And Courtesy. Be Polite To Everyone.”

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, …

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}

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