Examples using Maple to work with sequences

> a:=3*(-1)^n/n;

a := 3*(-1)^n/n

> seq(evalf(a),n=1..20);

-3., 1.500000000, -1., .7500000000, -.6000000000, ....
-3., 1.500000000, -1., .7500000000, -.6000000000, ....
-3., 1.500000000, -1., .7500000000, -.6000000000, ....

> with(wfucalc);

[eulerf, limitf, mygcd, nall, nallexp, nallquad, ne...
[eulerf, limitf, mygcd, nall, nallexp, nallquad, ne...
[eulerf, limitf, mygcd, nall, nallexp, nallquad, ne...

> seqf(a,n=1..20);

matrix([[n, 3*(-1)^n/n], [1., -3.000000000], [2., 1...

> plotseqf(a,n=1..20);

[Maple Plot]

> b:=3*(-1)^n/n!;

b := 3*(-1)^n/n!

> seq(b,n=1..20);

-3, 3/2, -1/2, 1/8, -1/40, 1/240, -1/1680, 1/13440,...
-3, 3/2, -1/2, 1/8, -1/40, 1/240, -1/1680, 1/13440,...
-3, 3/2, -1/2, 1/8, -1/40, 1/240, -1/1680, 1/13440,...

> seqf(b,n=1..10);

matrix([[n, 3*(-1)^n/n!], [1., -3.], [2., 1.5000000...

> plotseqf(b,n=1..10);

[Maple Plot]

> c:=product(2*k,k=1..n);

c := 1/2*2^(n+1)*GAMMA(n+1)

> seq(c,n=1..10);

2, 8, 48, 384, 3840, 46080, 645120, 10321920, 18579...

> d:=cos(n*Pi/2);

d := cos(1/2*n*Pi)

> seq(d,n=1..12);

0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1

> e:=(2*n+1)/(n^2+1);

e := (2*n+1)/(n^2+1)

> seqf(e,n=1..20);

matrix([[n, (2*n+1)/(n^2+1)], [1., 1.500000000], [2...

> seq(1.2^n,n=1..20);

1.2, 1.44, 1.728, 2.0736, 2.48832, 2.985984, 3.5831...
1.2, 1.44, 1.728, 2.0736, 2.48832, 2.985984, 3.5831...
1.2, 1.44, 1.728, 2.0736, 2.48832, 2.985984, 3.5831...

> seq(0.9^n,n=1..20);

.9, .81, .729, .6561, .59049, .531441, .4782969, .4...
.9, .81, .729, .6561, .59049, .531441, .4782969, .4...
.9, .81, .729, .6561, .59049, .531441, .4782969, .4...

> seq(0.5^n,n=1..20);

.5, .25, .125, .625e-1, .3125e-1, .15625e-1, .78125...
.5, .25, .125, .625e-1, .3125e-1, .15625e-1, .78125...
.5, .25, .125, .625e-1, .3125e-1, .15625e-1, .78125...

> seq((-0.4)^n,n=1..20);

-.4, .16, -.64e-1, .256e-1, -.1024e-1, .4096e-2, -....
-.4, .16, -.64e-1, .256e-1, -.1024e-1, .4096e-2, -....
-.4, .16, -.64e-1, .256e-1, -.1024e-1, .4096e-2, -....

> seq((-1.1)^n,n=1..20);

-1.1, 1.21, -1.331, 1.4641, -1.61051, 1.771561, -1....
-1.1, 1.21, -1.331, 1.4641, -1.61051, 1.771561, -1....
-1.1, 1.21, -1.331, 1.4641, -1.61051, 1.771561, -1....

> seq((-1)^n,n=1..20);

-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1...

> plotseqf((-1)^n,n=1..20);

[Maple Plot]

> seq(1^n,n=1..20);

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...