121k views
1 vote
Pls help to solve I don't know what is answer

Pls help to solve I don't know what is answer-example-1
User Ditto
by
8.3k points

1 Answer

4 votes

Answer:

2020

Explanation:

This is an example of what is called an "infinite continued fraction".

For the repeated fraction:

y = 2019 / (2 + 2019 / (2 + 2019 / (2 + 2019 / ...

We can rewrite using substitution:

y = 2019 / (2 + y)

Solving for y:

y (2 + y) = 2019

2y + y² = 2019

y² + 2y + 1 = 2020

(y + 1)² = 2020

y + 1 = ±√2020

y = -1 ± √2020

Since the repeated fraction must be positive, y = -1 + √2020.

Therefore:

x = (1 + y)²

x = (1 + -1 + √2020)²

x = 2020

User Jspooner
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories