Explicit Sequence

Integral calculus: sequences

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Complete Code

Download file: ExplicitSequence.pg

See Also

PG problem file

Explanation

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] ];

@seq = (
    "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"
);

$sequence = join(', ', @seq);

Setup

We set the test points to be positive integers to avoid errors when evaluating the answer. Even if you expect students to enter answers such as cos(pi * n) / n!, you should still restrict the domain to positive integers, because some students may simplify this to (-1)^n / n! and receive errors because the answer checker is substituting things such as n=0.5 into their formula.

For more explanation on the test_points see Formula Test Points

BEGIN_PGML
Find a formula for [`n^{th}`] term of the sequence [`[$sequence]`].

[`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.