A more thorough explanation:

The sum-of-the-years'-digits depreciation method is a formula used to estimate how much an asset will wear out or become obsolete over its useful life. This method is helpful in calculating the annual tax deduction for depreciation.

For example, let's say a company buys a machine for $10,000 and expects it to last for 5 years. Using the sum-of-the-years'-digits method, the company would calculate the depreciation expense for each year by multiplying the depreciable cost basis (the original cost minus the expected salvage value) by a fraction that decreases each year. The fraction is determined by adding up the digits of the years of useful life (5+4+3+2+1=15) and then dividing the remaining years of useful life at the beginning of each year by the total number of years of useful life (5/15, 4/15, 3/15, etc.).

This method results in larger depreciation expenses in the earlier years of an asset's life and smaller expenses in the later years, reflecting the fact that assets tend to lose value more quickly when they are new.