Sum of n Natural Numbers

// Method 1: Using for loop
let n = 10;
let sum = 0;

for (let i = 1; i <= n; i++) {
    sum += i;
}

console.log("Sum of first", n, "natural numbers:", sum);

// Method 2: Using formula (n × (n + 1)) / 2
let num = 10;
let sumFormula = (num * (num + 1)) / 2;
console.log("Using formula:", sumFormula);

// Method 3: Using while loop
let number = 10;
let total = 0;
let counter = 1;

while (counter <= number) {
    total += counter;
    counter++;
}

console.log("Using while loop:", total);

// Method 4: Using function
function sumNaturalNumbers(n) {
    let sum = 0;
    for (let i = 1; i <= n; i++) {
        sum += i;
    }
    return sum;
}

console.log("Using function:", sumNaturalNumbers(10));

// Method 5: Using reduce (functional approach)
function sumNaturalNumbersReduce(n) {
    return Array.from({length: n}, (_, i) => i + 1)
                 .reduce((sum, num) => sum + num, 0);
}

console.log("Using reduce:", sumNaturalNumbersReduce(10));

Sum of first 10 natural numbers: 55
Using formula: 55
Using while loop: 55
Using function: 55
Using reduce: 55

This program demonstrates different approaches to calculate sum of natural numbers.

Natural Numbers

Positive integers: 1, 2, 3, 4, 5, ...

Method 1: For Loop

Iterative approach:

javascript
let sum = 0;
for (let i = 1; i <= n; i++) {
    sum += i;
}

Compound Assignment

sum += i is shorthand for sum = sum + i

• +=: Addition assignment
• -=: Subtraction assignment
• *=: Multiplication assignment
• /=: Division assignment

Method 2: Mathematical Formula

Gauss's formula: n × (n + 1) / 2

javascript
let sum = (n * (n + 1)) / 2;

Pros:

• O(1) time complexity
• No loop needed
• Most efficient

Example:

Sum of 1 to 10 = (10 × 11) / 2 = 55

Method 3: While Loop

Condition-based iteration:

javascript
while (counter <= number) {
    total += counter;
    counter++;
}

Method 4: Function

Reusable code:

javascript
function sumNaturalNumbers(n) {
    let sum = 0;
    for (let i = 1; i <= n; i++) {
        sum += i;
    }
    return sum;
}

Method 5: Functional Approach (ES6)

Using array methods:

javascript
Array.from({length: n}, (_, i) => i + 1)
     .reduce((sum, num) => sum + num, 0);

Array.from(): Creates array from iterable

reduce(): Accumulates values

Time Complexity:

• Loop methods: O(n)
• Formula: O(1) - Best!

When to Use:

• Formula: Best performance

• Loop: Learning, flexible logic

• Reduce: Functional programming style