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Soloha48 [4]
3 years ago
6

Which of the following geometric series converges?

Mathematics
1 answer:
Mars2501 [29]3 years ago
8 0
All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is

Multiply both sides by r :

Subtract the latter sum from the first, which eliminates all but the first and last terms:

Solve for :

Then as gets arbitrarily large, the term will converge to 0, leaving us with

So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
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I need help with this (9x+7)+(x+3)
coldgirl [10]

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9x^2+34x+21

Step-by-step explanation:

distribute all the numbers

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What is the area of a circle with a radius of 6 inches?
Vika [28.1K]

Answer:

The answer to your question is   113.04 in²

Step-by-step explanation:

To solve this problem substitute the values in the formula and simplify.

Data

Area = ?

radius = 6 in

π = 3.14

Formula

Area = π x r²

Substitution

Area = (3.14) x (6)²

Simplification

Area = 3.14 x 36

Result

Area = 113.04 in²

7 0
3 years ago
The function f(x) = 2x + 510 represents the number of calories burned when exercising, where x is the number of hours spent exer
riadik2000 [5.3K]

Answer: 789 calories burned while combining diet with 2 hours of exercise

Step-by-step explanation:

we have that

f(x)=2x+510

g(x)=200x-125

we know that

(f+g)(x)=f(x)+g(x)

substitute

(f+g)(x)=2x+510+200x-125

(f+g)(x)=202x+385

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For x=2 hours

substitute

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therefore

The answer is

789 calories burned while combining diet with 2 hours of exercise

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