#把函数改成题干的####################
def fx(x):
    return 1/x


# 逐次分半梯形递推公式
def SplitTrapezoidal(a,b,err):
    count = 1
    t1 = (b-a)*(fx(a)+fx(b))/2
    print(f"t{count}={t1}")
    k = 1
    while True:
        tmp = 0
        for i in range(1, 2**(k-1)+1):
            tmp += fx(a + (b-a)*(2*i-1)/(2**k))
        t2 = t1/2+(b-a)*tmp/(2**k)
        count *= 2
        print(f"t{count}={t2}")
        if abs(t2-t1) < err:
            break
        t1 = t2
        k += 1
    return t2,k

#把范围ab换成题干的范围，err换成题干的精度要求############
if __name__ == "__main__":
    a = 1
    b = 3
    err = 1e-2
    result,k = SplitTrapezoidal(a, b, err)
    print(f"Result: {result},k={k}")