#Finite Sequences
a(n)=(n-1)/n
show(a(n))
print "n\ta(n)\ta(n).n()"
for n in range(1,10):
    print n,"\t",a(n),"\t",a(n).n()
print

#Infinite Series
show(sum([a(n).n() for n in range(1,5)]))
show(sum([a(n).n() for n in range(1,50)]))
show(sum([a(n).n() for n in range(1,500)]))
show(sum([a(n).n() for n in range(1,5000)]))
print

#Graph Of A Sequence
N=range(1,100)
A=[a(n) for n in N]
AN=zip(N,A)
plot(point(AN))
print

#Recursive Sequences
#a(1)=1, a(2)=1, a(n)=a(n-1)+a(n-2)
def fib(n):
    if(n==1 or n==2):
        return 1
    else:
        return fib(n-1)+fib(n-2)

N=range(1,30)
show([fib(n) for n in N])

F=[fib(n) for n in N]
FN=zip(N,F)
plot(point(FN))
for n in N:
    show(fib(n))