====== Question 11, 12 and 13, Exercise 4.7 ======
Solutions of Question 11, 12 and 13 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 11=====
Rewrite the sum using sigma notation: $-2+4-8+16-32+64$

** Solution. **

$$
-2 + 4 - 8 + 16 - 32 + 64 = \sum_{k=1}^{6} (-1)^k 2^k
$$

=====Question 12=====
Rewrite the sum using sigma notation: $\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4}+\frac{1}{4 \cdot 5}+$

** Solution. **

$$
\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \frac{1}{4 \cdot 5} + \ldots = \sum_{k=1}^{\infty} \frac{1}{k(k+1)}
$$

=====Question 13=====
Prove that $\sum_{k=1}^{n} k^{3}=\left[\frac{n(n+1)}{2}\right]^{3}$ FIXME

** Solution. **








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