morgaine816
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Find the summation. I know how to do these in general but I have never seen one with infinity. Please explain how to do this. Thank you.

Find the summation I know how to do these in general but I have never seen one with infinity Please explain how to do this Thank you class=

Respuesta :

[tex]\bf \textit{sum of an infinite geometric series}\\\\ S=\sum\limits_{i=0}^{\infty}\ a_1r^i\implies \cfrac{a_1}{1-r}\qquad \begin{cases} a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases}[/tex]

[tex]\bf -----------------------------\\\\ \sum\limits_{n=1}^{\infty}\ 1400(-0.5)^{n-1}\qquad \begin{cases} a_1=1400\\ r=-0.5\to -\frac{1}{2} \end{cases} \\\\\\ \cfrac{1400}{1-\left(-\frac{1}{2} \right)}\implies \cfrac{1400}{1+\frac{1}{2}}\implies \cfrac{1400}{\frac{3}{2}}\implies \cfrac{1400}{1}\cdot \cfrac{2}{3}\implies \cfrac{2800}{3}[/tex]

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