Sum of the terms of a geometric progression

Calculate $\sum_{n=0}^{17} 4\cdot(-2)^n$

Note that the first term that this is added is $n=0$, so, as we know, in order to be able to do the sum we change $m$ with $m=n+1$, so we have:

$$\left. \begin{array}{c} n=m-1 \\ n=17 \Rightarrow m=18 \\ n=0 \Rightarrow m=1 \end{array} \right\} \Rightarrow \sum_{n=0}^{17} 4\cdot(-2)^n = \sum_{m=1}^{18} 4\cdot(-2)^{m-1}$$

And in this way we find that $$\sum_{m=1}^{18} 4\cdot(-2)^{m-1}=\dfrac{4(1-(-2)^{18})}{1-(-2)}=\dfrac{4+2^{18}}{3}=\dfrac{262.148}{3}$$

$\sum_{n=0}^{17} 4\cdot(-2)^n =\dfrac{262.148}{3}$

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