Step by Step solution about How to resolve the algorithm Sum of a series step by step in the Kotlin programming language

Here's a detailed explanation of the Kotlin code:

1. The program calculates the sum of the series 1/1^2 + 1/2^2 + 1/3^2 + ... + 1/n^2, where n is a user-defined integer. The result is an approximation of the mathematical constant ζ(2) (zeta function evaluated at 2), which is known to be equal to π^2 / 6.

2. The program defines a variable n with the value 1000. This value can be changed to adjust the number of terms in the sum.

3. The sum is calculated using the sumByDouble function. This function takes a collection of numbers and applies a given lambda expression to each element, returning the sum of the results. In this case, the lambda expression 1.0 / (it * it) is used to calculate 1/n^2 for each value of n in the range 1 to n.

4. The result of the sum is stored in a variable called sum.

5. The program prints the calculated sum to the console.

6. Finally, the program prints the value of ζ(2) calculated using the mathematical formula, which is π^2 / 6.

By comparing the calculated sum with the exact value of ζ(2), you can observe how close the approximation is for the given number of terms in the series.

// version 1.0.6

fun main(args: Array<String>) {
    val n = 1000
    val sum = (1..n).sumByDouble { 1.0 / (it * it) }
    println("Actual sum is $sum")
    println("zeta(2)    is ${Math.PI * Math.PI / 6.0}")
}