Question 3 and 4, Exercise 4.7

Solutions of Question 3 and 4 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.

Evaluate the sum: $\sum_{k=0}^{5} 2^{k}$

Solution.

$$\begin{align*} \sum_{k=0}^{5} 2^{k} &= 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 \\ &= 1 + 2 + 4 + 8 + 16 + 32 \\ &= 63 \end{align*}$$

Evaluate the sum: $\sum_{k=0}^{9} \pi k$

Solution.

$$\begin{align*} \sum_{k=0}^{9} \pi k &= \pi(0) + \pi(1) + \pi(2) + \pi(3) + \pi(4) + \pi(5) + \pi(6) + \pi(7) + \pi(8) + \pi(9) \\ &= 0 + \pi + 2\pi + 3\pi + 4\pi + 5\pi + 6\pi + 7\pi + 8\pi + 9\pi \\ &= 45\pi \end{align*}$$

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