# Finding the maximum pyramidal number by recursion in python

Python is a versatile programming language that offers multiple ways to solve problems. In this article, we will explore different approaches to finding the maximum pyramidal number by recursion in Python.

## Approach 1: Using a Recursive Function

One way to solve this problem is by using a recursive function. We can define a function that takes an input number and recursively calculates the maximum pyramidal number.

``````def find_max_pyramidal_number(n):
if n == 1:
return 1
else:
return n + find_max_pyramidal_number(n-1)``````

In this code, the function takes an input number ‘n’ and checks if it is equal to 1. If it is, the function returns 1. Otherwise, it recursively calls itself with ‘n-1’ and adds ‘n’ to the result.

## Approach 2: Using a Loop

Another approach to solving this problem is by using a loop. We can iterate from 1 to the input number and calculate the maximum pyramidal number.

``````def find_max_pyramidal_number(n):
result = 0
for i in range(1, n+1):
result += i
return result``````

In this code, we initialize a variable ‘result’ to 0. Then, we iterate from 1 to ‘n’ using a loop and add each number to ‘result’. Finally, we return the calculated result.

## Approach 3: Using the Formula

The third approach involves using a mathematical formula to calculate the maximum pyramidal number. The formula for the sum of the first ‘n’ natural numbers is (n * (n + 1)) / 2.

``````def find_max_pyramidal_number(n):
return (n * (n + 1)) // 2``````

In this code, we directly calculate the maximum pyramidal number using the formula. We multiply ‘n’ with ‘n+1’ and divide the result by 2. The double forward slash ‘//’ is used for integer division.

After exploring these three approaches, it is evident that the third option, using the formula, is the most efficient and concise solution. It avoids the overhead of function calls and loops, resulting in faster execution. Therefore, using the formula is the recommended approach for finding the maximum pyramidal number by recursion in Python.

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### 4 Responses

1. Clyde says:

Approach 3 seems efficient, but what about the elegance of recursion in Approach 1? Discuss!

Approach 3 seems like a math wizards dream! Who needs loops when you have formulas? #PyramidPower

3. Azariah Cummings says:

Approach 3 is like finding a shortcut to unlock the treasure! Who doesnt love that? #FormulaMagic

4. Charley says:

Approach 1 seems cool, but who needs recursion when you can loop it out in Approach 2? 🔄🐍