Question

Calculați:(-2)¹ + (-2)² + (-2)³ + ... + (-2)¹⁰⁰

Answer 1

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.

Step-by-step 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

`\begin{gathered} S_n=(a(1-r^n))/(1-r) \\ put\text{ n = 100} \\ S_(100)=(-2(1-(-2)^(100)))/(1-(-2)) \\ S_(100)=-(2)/(3)(1-(-2)^(100)) \end{gathered}`

Therefore, the sum of the given series is

`\begin{gathered} -(2)/(3)(1-(-2)^(100)) \\ or \\ -(2)/(3)(1-2^(100)) \end{gathered}`