Infinitely many elevators!

Calculus Level pending

There are two companies, A and B. the first company, A, manufactures elevators and the other, company B, that ordered 50 of the same exact elevators from company A. Company A, the one responsible for manufacturing elevators, ran into a problem. Company A created only 96% of the original designed elevator for the first then stopped and started the manufacturing of the second elevator. For the second elevator they designed, Company A made only half of the missing details as the first. (48% of the original design). Additionally, half of the details for the third (24%), half for the fourth(12%), so on, infinitely many times. for each elevator they made different details. When they made details for infinitely many elevators, they started to plug details together. (0.96+0.48+0.24+0.12+...)

Did they fulfill the order?

No, they made some; however, it was not enough; No, they never made a single elevator; Yes, because they made infinitely many elevators; Yes, because they made enough, but not infinitely many;

1 solution

Maksym Karunos
Aug 6, 2019

The problem can be represented with an infinite geometric series. The first element is 1, the ration is $\frac{1}{2}$

$\displaystyle\sum_{n=1}^{\infty} (0.96)(0.5)^{k-1} = 1.92$

As 50 > 1.92

$\therefore$ No, they made some; however, it was not enough;

@Maksym Karunos You make a mistake, the common ratio is not 0.96, it should be 0.5. Therefore the equation should be like this $\sum _{ k=1 }^{ \infty }{ \left( 0.96 \right) { \left( 0.5 \right) }^{ k-1 } } =1.92$ The answer is still correct, but please check the question before posting it

Isaac YIU Math Studio - 1 year, 10 months ago

Thanks. Resolved.

Maksym Karunos - 1 year, 10 months ago

Infinitely many elevators!

1 solution

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