contestada

Consider the geometric series: 1000, 500, 250, 125,.
Question: A. Does this sequence converge or diverge?
B. What is the sum of the first 10 terms of the series?
C. What is the sum of the first 30 terms of the series?
D. What do these two sums tell you about the series as it continues? ​

Respuesta :

sopiyamgr2468

Answer:

a diverge

b512000

c1000(2^30-1)

d

Step-by-step explanation:

t10=ar^9

=1000*2^9

s30=a(r^n-1)/r-1

=1000(2^30-1)/2-1

The geometric series given as 1000, 500, 250, 125,... is seen to be; Convergent.

What is divergent or convergent series?

A series is said to be divergent if it doesn't converge at any finite point. However, a series is said to be convergent if it converges at a finite point.

In this question, we see the series progressively reducing by one quarter of the previous number. Thus, it means that the sequence will converge close to zero and as such we can say taht the sequence is convergent.

Formula for sum of geometric series is;

Sₙ = a(1 - rⁿ)/(1 - r)

Thus;

S₁₀ = 1000(1 - 0.5¹⁰)/(1 - 0.5)

S₁₀ = 1998.05

Sum of first 30 terms is;

S₃₀ = 1000(1 - 0.5³⁰)/(1 - 0.5)

S₃₀ = 2000

Read more about convergent and divergent series at; https://brainly.com/question/15415793

#SPJ2

Otras preguntas