Pow

Math.Pow

using System;
using System.Linq;

public static class Grains
{
    public static double Square(int i)
    {
        if (i is <= 0 or > 64)
            throw new ArgumentOutOfRangeException(nameof(i));

        return Math.Pow(2, i - 1);
    }

    public static double Total()
    {
        return Enumerable.Range(1, 64).Sum(Square);
    }
}

Other languages may have an exponential operator such as ** or ^ to raise a number by a specified power. C# does not have an exponential operator, but uses the Math.Pow method.

Pow is nicely suited to the problem, since we start with one grain and keep doubling the number of grains on each successive square. 1 grain is Math.Pow(2, 0), 2 grains is Math.Pow(2, 1), 4 is Math.Pow(2, 2), and so on. So, to get the right exponent, we subtract 1 from the square number i.

For Total we can reuse Square by passing it 1 through 64 and summing the result from each call. This example uses Enumerable.Range to iterate from 1 through 64 and chains it to the Sum method.

Shortening

When the body of an if statement is a single line, both the test expression and the body could be put on the same line, like so

if (i is <= 0 or > 64) throw new ArgumentOutOfRangeException(nameof(i));

The C# Coding Conventions advise to write only one statement per line in the layout conventions section, but the conventions begin by saying you can use them or adapt them to your needs. Your team may choose to overrule them.

When the body of a function is a single expression, the function can be implemented as a expression-bodied member, like so

public static double Total() =>
    Enumerable.Range(1, 64).Sum(Square);

or

public static double Total() => Enumerable.Range(1, 64).Sum(Square);