Final answer:
The question involves using integration to approximate the sum of a convergent series in mathematics, by comparing the series to the integral of a related function and calculating this integral.
Step-by-step explanation:
The student is dealing with a convergent series in mathematics and is asked to use an integration technique to find its sum. To tackle this problem, we would compare the given series Σ 7/8k⁴ with a corresponding integral. The usual process involves setting up the integral of a function closely related to the terms of the series, such as f(x) = 7/8x⁴ over the interval from 1 to infinity, and then determining the integral's value, which would approximate the sum of the series.