Question

Занайдіть суму нескінченоої геометричної прогресії 9; 3; 1; ... .

Answer 1

Ответ:

S=13,5

Объяснение:

q=1/3

S=b1/(1-q)=9/(1-1/3)=9/(2/3)=9*3/2=13,5

Answer 2

Finding the Sum of an Infinite Geometric Progression

To find the sum of an infinite geometric progression with a common ratio (r) between -1 and 1, we can use the formula:

Sum = a / (1 - r)

Where: - a is the first term of the progression - r is the common ratio

In this case, the first term (a) is 9 and the common ratio (r) is 1/3.

Calculation

Using the formula, we can calculate the sum:

Sum = 9 / (1 - 1/3)

Sum = 9 / (2/3)

Sum = 9 * (3/2)

Sum = 27 / 2

So, the sum of the infinite geometric progression 9, 3, 1, ... is 27/2. This means that the sum of the progression is 13.5.

This information is based on the formula for the sum of an infinite geometric progression and the specific values provided for the first term and the common ratio