Question

Запишіть суму нескінченої геометричної прогресії 125;-25;5;....​

Answer 1

Ответ:

S=104,17

Пошаговое объяснение:

q= -1/5

S=b1/(1-q)=125/(1+1/5)=125/(6/5)=125*5/6=104,17

Answer 2

Sum of an Infinite Geometric Progression

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

S = a / (1 - r)

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

In this case, the given geometric progression is 125, -25, 5, ...

Let's find the first term (a) and the common ratio (r):

The first term (a) is 125.

The common ratio (r) can be found by dividing any term by its previous term. Let's calculate it:

- r = -25 / 125 = -0.2

Now, we can substitute the values of a and r into the formula to find the sum (S):

S = 125 / (1 - (-0.2))

Simplifying the expression:

S = 125 / (1 + 0.2)

S = 125 / 1.2

S = 104.1667

Therefore, the sum of the infinite geometric progression 125, -25, 5, ... is approximately 104.1667.