Auxiliary Procedure Definitions (execute, but do not modify)

>	AnimateSeries := proc( series,

>	domain::name=range(constant),

>	psums::list(nonnegint) )

>	local NULL

>	, F          # limit of infinite sum

>	, P          # final plot data structure [returned]

>	, plot_opts  # optional arguments to plot command

>

;

>	if nargs>3

>	then plot_opts := args[4..nargs]

>	else plot_opts := NULL

>

end if;

>	if nops(series)=2 and op(0,series)<>`Sum`

>

then

>	error "invalid first argument, must an unevaluated series, received",

>

series

>

end if;

>	F := value( series );

>	P := display( [seq(

>	plot( [subsop([2,2,2]=N,series), F ],

>	domain, plot_opts, title="Partial Sum: N="||N ),

>	N=psums )],

>	insequence=true );

>

return P

>

end proc:

Example 1

>	Series1 := Sum( x^k, k=0..infinity );

>	AnimateSeries( Series1, x=-2..2, list_N3, y=-10..100, discont=true );

>

Example 2

>	Series2 := Sum( (-1)^n*x^n/n, n=1..infinity );

>	AnimateSeries( Series2, x=-2..2, list_N3, y=-10..100, discont=true );

>

Example 3

>	Series3 := Sum( n*x^(n-1), n=1..infinity );

>	AnimateSeries( Series3, x=-2..2, list_N3, y=-20..100, discont=true );

>

Example 4

>	Series4 := Sum( (-1)^n*x^(2*n)/(2*n)!, n=0..infinity );

>	AnimateSeries( Series4, x=-5*Pi..5*Pi, list_N1, y=-2..2, discont=true );

>

Example 5

>	Series5 := Sum( (-(x+x^2))^n, n=0..infinity );

>	AnimateSeries( Series5, x=-5..5, list_N1, y=0..2, discont=true );

>

>	solve( abs(x+x^2) < 1, {x} );

>	plot( [abs(x+x^2),1], x=-3..3 );

>

Example 6

>	Series6 := Sum( (-1)^n*x^n/n, n=1..infinity );

>	AnimateSeries( Series6, x=-5..5, list_N1, y=-2..2, discont=true );

>

Example 7

>	Series7 := Sum( n*(n-1)*x^(n-1), n=2..infinity );

>	AnimateSeries( Series7, x=-3..3, list_N2, y=-10..10, discont=true );

>

>	value( Series7 );

>

Example 8

>	Series8 := Sum( (x-5)^n/(2^n*n*(n+1)), n=1..infinity );

>	AnimateSeries( Series8, x=0..8, list_N3, y=-4..20, discont=true );

>

>	value( Series8 );

>