Sequences and Series

with graphs

>	with(plots):

>	points:=array(1..40);

>	for i from 1 to 40 do

>	points[i]:=(i,(4/5)^i):

>

end do:

>	pointss:=convert(points,listlist):

>	pointplot(pointss,symbol=circle,symbolsize=12,color=red);

>	Limit((4/5)^n,n=infinity);

>

value(%);

>	sums:=array(1..40);

>	for i from 1 to 40 do

>	sums[i]:=(i,sum((4/5)^n,n=1..i)):

>

end do:

>	sumss:=convert(sums,listlist):sums:=array(1..40);

>	pointplot(sumss,symbol=circle,symbolsize=12,color=red);

>	Sum((4/5)^n,n=1..40);

>

value(%);

>

evalf(%);

>	evalf(sum((4/5)^n,n=1..100));

>	evalf(sum((4/5)^n,n=1..1000));

>	evalf(sum((4/5)^n,n=1..infinity));

>	points2:=array(1..40);

>	for i from 1 to 40 do

>	points2[i]:=(i,(2^i)/i!):

>

end do:

>	points2s:=convert(points2,listlist):

>	pointplot(points2s,symbol=circle,symbolsize=12,color=red);

>	Limit((2^n)/n!,n=infinity);

>

value(%);

>	sums2:=array(1..40);

>	for i from 1 to 40 do

>	sums2[i]:=(i,sum((2^n)/n!,n=1..i)):

>

end do:

>	sums2s:=convert(sums2,listlist):

>	pointplot(sums2s,symbol=circle,symbolsize=12,color=red);

>	Sum((2^n)/n!,n=1..40);

>

value(%);

>

evalf(%);

>	Sum((2^n)/n!,n=1..100);

>

evalf(%);

>	sum((2^n)/n!,n=1..infinity);

>

evalf(%);

>	sum((2^n)/n!,n=0..infinity);

>	points3:=array(1..40);

>	for i from 1 to 40 do

>	points3[i]:=(i,20*sin(i)/i^2):

>

end do:

>	points3s:=convert(points3,listlist):

>	pointplot(points3s,symbol=circle,symbolsize=12,color=red);

>	Limit(20*sin(n)/n^2,n=infinity);

>

value(%);

>

i:='i';

>	sums3:=array(1..40);

>	for i from 1 to 40 do

>	sums3[i]:=(i,sum(20*sin(n)/n^2,n=1..i)):

>

end do:

>	sums3s:=convert(sums3,listlist):

>	pointplot(sums3s,symbol=circle,symbolsize=12,color=red);

>	Sum(20*sin(n)/n^2,n=1..40);

>

value(%);

>

evalf(%);

>	evalf(sum(20*sin(n)/n^2,n=1..40));

>	evalf(sum(20*sin(n)/n^2,n=1..100));

>	evalf(sum(20*sin(n)/n^2,n=1..1000));

>	evalf(sum(20*sin(n)/n^2,n=1..10000));

>	evalf(sum(20*sin(n)/n^2,n=1..20000));

>	evalf(sum(20*sin(n)/n^2,n=1..infinity));

>	points4:=array(1..40);

>	for i from 1 to 40 do

>	points4[i]:=(i,(-1)^i*(i^5/exp(i))):

>

end do:

>	points4s:=convert(points4,listlist):

>	pointplot(points4s,symbol=circle,symbolsize=12,color=red);

>	Limit((-1)^n*(n^5/exp(n)),n=infinity);

>

value(%);

>	sums4:=array(1..40);

>	for i from 1 to 40 do

>	sums4[i]:=(i,sum((-1)^n*(n^5/exp(n)),n=1..i)):

>

end do:

>	sums4s:=convert(sums4,listlist):sums4:=array(1..40);

>	pointplot(sums4s,symbol=circle,symbolsize=12,color=red);

>	sums5:=array(20..40);

>	for i from 20 to 40 do

>	sums5[i]:=(i,sum((-1)^n*(n^5/exp(n)),n=1..i)):

>

end do:

>	sums5s:=convert(sums5,listlist):sums5:=array(20..40);

>	pointplot(sums5s,symbol=circle,symbolsize=12,color=red);

>	Sum((-1)^n*(n^5/exp(n)),n=1..40);

>

value(%);

>

evalf(%);

>	evalf(sum((-1)^n*(n^5/exp(n)),n=1..100));

>	evalf(101^5/exp(101));

>