Sunday, October 27, 2013
Integral bounds of a series
Suppose
an=f(n) where f is a decreasing and positive function. |
∫∞1f(x)dx is finite, |
∫∞1f(x)dx≤∞∑n=1an≤a1+∫∞1f(x)dx |
You can find more information at Calculus Two: Sequences and Series.
Suppose
an=f(n) where f is a decreasing and positive function. |
∫∞1f(x)dx is finite, |
∫∞1f(x)dx≤∞∑n=1an≤a1+∫∞1f(x)dx |
You can find more information at Calculus Two: Sequences and Series.