====== 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. 

=====Question 3=====
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*}




=====Question 4=====
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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