Question

Найдите сумму бесконечной геометрической прогрессии 24; -12; 6;... как это сделать?

Answer 1

Члены:
b1= 24
b2= -12
знаменатель г. пр. q= 24/-12 = -2
сумма г. пр. S= b1 / 1-q = 24 / 1-(-2) = 24 / 3 = 8

Answer 2

Calculating the Sum of an Infinite Geometric Progression

To find the sum of an infinite geometric progression, we can use the formula:

Sum of Infinite Geometric Progression (S): \[ S = \frac{a}{1 - r} \]

Where: - \( a \) = the first term of the progression - \( r \) = the common ratio

Applying the Formula to the Given Geometric Progression

In the given geometric progression: 24, -12, 6, ...

We can identify: - \( a = 24 \) - \( r = -12/24 = -0.5 \)

Using the formula, we can calculate the sum: \[ S = \frac{24}{1 - (-0.5)} \]

\[ S = \frac{24}{1.5} = 16 \]

So, the sum of the given infinite geometric progression is 16.

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