Given:
a series is given as (-2)¹ + (-2)² + (-2)³ + ... + (-2)¹⁰⁰
Find:
we have to find the sum of the given series.
Explanation:
The given series is geometric series with first term a = (-2)¹ , common ratio (r) = -2.
The sum of the given geometric series is
[tex]\begin{gathered} S_n=\frac{a(1-r^n)}{1-r} \\ put\text{ n = 100} \\ S_{100}=\frac{-2(1-(-2)^{100})}{1-(-2)} \\ S_{100}=-\frac{2}{3}(1-(-2)^{100}) \end{gathered}[/tex]Therefore, the sum of the given series is
[tex]\begin{gathered} -\frac{2}{3}(1-(-2)^{100}) \\ or \\ -\frac{2}{3}(1-2^{100}) \end{gathered}[/tex]
