SharedMTHS120.ipynbOpen in CoCalc
MTHS120 - plotting sequences

Plotting sequences

We plot the sequence an=cos(n)/na_n=\cos(n)/n for n=1,2,,100n=1,2,\dots,100.

p = points([(n,cos(n)/n) for n in range(1,101)])
show(p)

We add the graphs of the functions given by f(x)=1/xf(x)=1/x and g(x)=1/xg(x)=-1/x to illustrate that from limx1/x=0\lim_{x\to\infty}1/x=0 we can deduce limnan=0\lim_{n\to\infty}a_n=0.

x = var('x')
p += plot(1/x,x,1,100,color='red') + plot(-1/x,x,1,100,color='red')
show(p)