GeometricSeries.kt

// https://en.wikipedia.org/wiki/Geometric_series

/**
 * @param a is coefficient
 * @param r is the common ratio
 * @return sum of a*r.pow(n) + a*r.pow(n - 1) + ... + a*r.pow(m - 1) + a*r.pow(m)
 */
fun getSumOfGeometricSeries(
    a: Int = 1,
    r: Double = 10.0,
    m: Int = 0,
    n: Int,
): Double {
    require(m >= 0) { "m($m) is negative!" }
    require(n >= m) { "n($n) < m($m)!" }
    return r * a * (r.pow(m) - r.pow(n)) / (1.0 - r)
}

fun getSumOfGeometricSeries10(
    a: Int = 1,
    m: Int = 0,
    n: Int,
): Double {
    require(m >= 0) { "m($m) is negative!" }
    require(n >= m) { "n($n) < m($m)!" }
    return 10.0.pow(m + 1) * a * (1 - 10.0.pow(n - m)) / -9.0
}

/**
 * @param a is coefficient
 * @param r is the common ratio
 * @param sum - value of a*r.pow(n) + a*r.pow(n - 1) + ... + a*r.pow(1)
 * @return n
 */
fun getPowerOfGeometricSeries(
    a: Int = 1,
    r: Double = 10.0,
    sum: Double
): Double {
    return kotlin.math.log(1 - sum * (1.0 - r) / (a * r), r)
}

fun getPowerOfGeometricSeries10(
    a: Int = 1,
    sum: Double
): Double {
    return kotlin.math.log10(1 + (sum * 9.0) / (a * 10.0))
}