Question

1/2+1/4+1/8найти сумму геометрической прогрессии

Answer 1

4/8+2/8+1/8=7/8 кажется так

Answer 2

Finding the Sum of a Geometric Progression

To find the sum of a geometric progression, we need to know the first term, the common ratio, and the number of terms in the progression. In this case, we have the following geometric progression: 1/2, 1/4, 1/8.

Let's calculate the sum using the formula for the sum of a geometric progression:

Sum of a Geometric Progression Formula: \[S_n = \frac{a(1 - r^n)}{1 - r}\]

Where: - \(S_n\) is the sum of the geometric progression - \(a\) is the first term of the progression - \(r\) is the common ratio - \(n\) is the number of terms in the progression

In our case, the first term \(a\) is 1/2, the common ratio \(r\) is 1/2, and the number of terms \(n\) is 3.

Let's substitute these values into the formula and calculate the sum:

\[S_3 = \frac{\frac{1}{2}(1 - \left(\frac{1}{2}\right)^3)}{1 - \frac{1}{2}}\]

Simplifying the equation:

\[S_3 = \frac{\frac{1}{2}(1 - \frac{1}{8})}{\frac{1}{2}}\]

\[S_3 = \frac{\frac{1}{2} \cdot \frac{7}{8}}{\frac{1}{2}}\]

\[S_3 = \frac{7}{8}\]

Therefore, the sum of the geometric progression 1/2, 1/4, 1/8 is 7/8.

Answer

The sum of the geometric progression 1/2, 1/4, 1/8 is 7/8.