Define to be the left-endpoint Riemann sum with equal subintervals for

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Define

S_n

to be the left-endpoint Riemann sum with

n

equal subintervals for

\displaystyle \int_{0}^{1} x^{3}\,dx

. Evaluate

\displaystyle \lim_{n\to\infty} S_n