Question 9 and 10, Exercise 4.7

Solutions of Question 9 and 10 of Exercise 4.7 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Rewrite the sum using sigma notation: $\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}+\dots$

Solution.

$$\frac{1}{2} + \frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6} +... = \sum_{k=1}^{\infty}\frac{k}{k+1}$$

Rewrite the sum using sigma notation: $3+6+9+12+15$

Solution.

$$3+6+9+12+15=\sum_{k=1}^{5}3k$$

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