Integral calculus: sequences
Download file: ExplicitSequence.pg
DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');
Preamble
These standard macros need to be loaded.Context()->variables->are(n => 'Real');
$answer = Compute('(-1)^n / n!');
$answer->{test_points} = [ [1], [2], [3], [4], [5], [6] ];
Setup
The answer is a formula involving factorials that are only defined for positive integers. So set the test points to be positive integers to avoid errors when evaluating the answer.
For more explanation on test_points see Formula
Test Points
BEGIN_PGML
Find a formula for [`n^{th}`] term of the sequence [`a_0 = 1`], [`a_1 = -1`].
[`a_2 = \frac{1}{2}`], [`a_3 = -\frac{1}{6}`], [`a_4 = \frac{1}{24}`],
[`a_5 = -\frac{1}{120}`], [`\ldots`].
[`a_n =`] [_]{$answer}{20}
END_PGML
Statement
This is the problem statement in PGML.BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION ENDDOCUMENT();
Solution
A solution should be provided here.