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Find the sum of the geometric series 9000-900 +...+ 0.009

Sagot :

Lanuel

Based on the calculations, the sum of this geometric series is equal to 9,990.

The standard form of a geometric series.

Mathematically, the standard form of a geometric series can be represented by the following expression:

[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]

Where:

  • a₁ is the first term of a geometric series.
  • r is the common ratio.

How to calculate the sum of a geometric series?

Also, the sum of a geometric series is given by this mathematical expression:

[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]

Given the following data:

  • First term, a = 9000.
  • Common ratio, r = 900/9000 = 0.1

Substituting the given parameters into the formula, we have;

[tex]S=\frac{9000(1-0.1^3)}{1-0.1}\\\\S=\frac{9000(1-0.001)}{1-0.1}[/tex]

S = 9000(0.999)/0.9

S = 8,991/0.9

S = 9,990.

Read more on geometric series here: brainly.com/question/12630565

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