Summing the Fibonacci Sequence

An image from nature (by ...). The golden ratio appears in here and is closely related to the Fibonacci sequence.
An image from nature (by Sustainable San Mateo). The golden ratio approximately (this is a topic for discussion) appears in here and is closely related to the Fibonacci sequence.

Consider the following problem (Project Euler, Problem #2):

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Solving this problem by using a programming language is relatively easy and requires only looping through the sequence. How can you tackle this problem without the need for a computer? Spoiler alert: there is only one final step in which we will use a calculator.

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Project Euler using Scala: Problem #1

In this last post I gave a short introduction to Scala. In this article, I will show you the strength of Scala for solving one of the mathematical problems posted on Project Euler. The problem description is as follows:

Multiples of 3 and 5

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.

I will first show you a naive approach and then I will show you a better approach.

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