python计算 1/2+2/3+3/5+5/8+8/13…的前10项的和。

这是一个典型的无穷递归序列求和的问题，其中每一项都是两个相邻素数之比。我们可以编写一个Python程序来计算前10项的和。首先，我们需要生成一系列这样的分数，并找到它们对应的前10对连续的素数。下面是一个简单的实现：

def is_prime(n):
    if n <= 1:
        return False
    for i in range(2, int(n**0.5) + 1):
        if n % i == 0:
            return False
    return True

def fibonacci_like_sum(n):
    primes = [2]  # Start with the first prime number
    sum_of_terms = 0
    count = 0
    
    while count < n:
        next_prime = primes[-1]
        
        # Find the next consecutive prime
        for num in range(primes[-1], primes[-1]*next_prime, next_prime):  # Skip multiples of the current prime
            if is_prime(num):
                primes.append(num)
                break
        
        # Calculate the term and add it to the sum
        term = primes[count+1] / primes[count]
        sum_of_terms += term
        count += 1
        
    return sum_of_terms

# Calculate the sum of the first 10 terms
sum_10_terms = fibonacci_like_sum(10)
print(f"The sum of the first 10 terms is: {sum_10_terms}")

这个脚本会打印出前10项的和。请注意，由于涉及到大量的素数检查，实际运行时可能会比较慢。