#1)
a(n)=(n-1)/n
a(n)
|
|
print "n\ta(n)\ta(n).n()"
for n in range(1,10):
print n,"\t",a(n),"\t",a(n).n()
n a(n) a(n).n() 1 0 0.000000000000000 2 1/2 0.500000000000000 3 2/3 0.666666666666667 4 3/4 0.750000000000000 5 4/5 0.800000000000000 6 5/6 0.833333333333333 7 6/7 0.857142857142857 8 7/8 0.875000000000000 9 8/9 0.888888888888889 n a(n) a(n).n() 1 0 0.000000000000000 2 1/2 0.500000000000000 3 2/3 0.666666666666667 4 3/4 0.750000000000000 5 4/5 0.800000000000000 6 5/6 0.833333333333333 7 6/7 0.857142857142857 8 7/8 0.875000000000000 9 8/9 0.888888888888889 |
#discrete
N=range(1,100)
A=[a(n) for n in N]
AN=zip(N,A)
plot(point(AN))
|
|
show(sum([a(n) for n in range(1,10)]).n())
show(sum([a(n) for n in range(1,100)]).n())
show(sum([a(n) for n in range(1,1000)]).n())
|
|
#not discrete
N=range(1,100)
A=[a(n) for n in N]
AN=zip(N,A)
g=Graphics()
g+=point(AN)
for k in range(1,len(AN)):
g+=line((AN[k-1],AN[k]))
show(g)
|
|
#2)
b(n)=(-1)^(n+1)*2/n
b(n)
|
|
print "n\tb(n)\tb(n).n()"
for n in range(1,10):
print n,"\t",b(n),"\t",b(n).n()
n b(n) b(n).n() 1 2 2.00000000000000 2 -1 -1.00000000000000 3 2/3 0.666666666666667 4 -1/2 -0.500000000000000 5 2/5 0.400000000000000 6 -1/3 -0.333333333333333 7 2/7 0.285714285714286 8 -1/4 -0.250000000000000 9 2/9 0.222222222222222 n b(n) b(n).n() 1 2 2.00000000000000 2 -1 -1.00000000000000 3 2/3 0.666666666666667 4 -1/2 -0.500000000000000 5 2/5 0.400000000000000 6 -1/3 -0.333333333333333 7 2/7 0.285714285714286 8 -1/4 -0.250000000000000 9 2/9 0.222222222222222 |
show(sum([b(n) for n in range(1,10)]).n())
show(sum([b(n) for n in range(1,100)]).n())
show(sum([b(n) for n in range(1,1000)]).n())
|
|
|
|