Chapter 8: Infinite Sequences and Series
Section 8.3: Convergence Tests
Determine if the series ∑n=2∞n3−1n! diverges, converges absolutely, or converges conditionally.
If it converges conditionally, determine if it also converge absolutely.
Applying the Ratio test, compute
from which it follows that the given series converges absolutely.
The most efficient way to implement the Ratio test in Maple, is to define the general term an as a function an.
Context Panel: Assign Function
an=n3−1n!→assign as functiona
Calculus palette: Limit operator
Context Panel: Evaluate and Display Inline
limn→∞an+1an = 0
This is series that Maple can sum exactly, and that also establishes its absolute convergence, provided the evidence of a computer computation is taken as sufficient mathematical proof.
Expression palette: Summation template
∑n=2∞an = 1+4⁢ⅇ
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