1.计算下列多项式之和

    1+1/2+1/3+1/4+······+1/100 =

sum = 0
for i in range(1,101):
    sum += (1 / i)
print(sum)

结果：

2.  1-1/2+1/3-1/4+1/5·····1/n =

sum = 0
for i in range(1,101):
    if i % 2 == 1:
        sum += (1 / i)
    if i % 2 == 0:
        sum -= (1 / i)
print(sum)

结果：

3.  1+1/(1+2)+1/(1+2+3)+····+1/(1+2+3+···+n) = 

sum = 0
fenmu = 0
for i in range(1,101):
    fenmu += i
    sum += (1 / fenmu)
print(sum)

结果：

4.  计算a+aa+aaa+a···a前6项之和（a = 2)

sum = 0
a = int(input("请输入一个数字:"))
for i in range(6):
    sum += a
    a += a * 10
print(sum)

结果：

5.  用泰勒级数计算e的近似值，直到最后一项小于1e-6为止，e = 1+1/1!+1/2!+1/3!+···+1/n!

e = 1
fenmu = 1
i = 1
while 1 / fenmu >= 1e-6:
    e += (1 / fenmu)
    i += 1
    fenmu *= i
print(e)

结果：

6.   计算Π的公式为，Π/4 = 1-1/3+1/5-1/7+···

a = 0
i = 1
xiang = 2
while 1 / i >= 1e-6:
    a += 1 /(i * (-1)**xiang) #** 的优先级高于- ，所以要加（）
    xiang += 1
    i += 2
Π = 4 * a
print(Π)

结果：

7.打印空心菱形

n = int(input("请输入您要打印的空心菱形的行数(只可输入奇数）："))
h = (n + 1) // 2
for i in range(h):
    for j in range(h - i - 1):
        print(" ",end="")
    for j in range(2 * i + 1):
        if j == 0 or j == 2 * i:
            print("*",end ="")
        else:
            print(" ",end="")
    print()
for i in range(h - 2,-1,-1):
    for j in range(h - i - 1):
        print(" ",end="")
    for j in range(2 * i + 1):
        if j == 0 or j == 2 * i:
            print("*",end ="")
        else:
            print(" ",end="")
    print()

结果：