Question

Знайдіть суму нескінченної геометричної прогресії (Bn), якщо B3 = 0.8, і В4 = 0.16

Answer 1

Так як B3 = 0.8, а В4 = 0.16, то q=В4/В3=0,2 (так як це геометрична прогресія).
тоді В2=В3/q=4
B1=B2/q=20
S=B1/(1-q)=20/0,8=25

Answer 2

 


$q = b4 : b3 = 0,16 : 0,8 = 0,2$
$b3=b1q^2$
$b1=b3:q^2 = 0,8: 0,04 = 20$
$S=b1:(1-q)=20:(1-0,2)=20 : 0,8 = 25$

Answer 3

Calculating the 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 infinite geometric progression - a is the first term of the progression - r is the common ratio of the progression

In this case, we are given the third and fourth terms of the progression, which allows us to find the common ratio.

Finding the Common Ratio (r)

The common ratio r can be found using the given terms B3 and B4:

B4 = B3 * r

Given: - B3 = 0.8 - B4 = 0.16

We can use these values to solve for the common ratio r:

0.16 = 0.8 * r
r = 0.16 / 0.8
r = 0.2

So, the common ratio r is 0.2.

Calculating the Sum (S)

Now that we have the common ratio, we can use the formula to calculate the sum S:

S = a / (1 - r)

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

However, since we are not given the first term of the progression, we cannot directly calculate the sum of the infinite geometric progression without this information.

If you have the value of the first term (a), please provide it, and I can help you calculate the sum of the infinite geometric progression.