Check Triangular Number in Python

What You’ll Learn

A triangular number is the total of stacked rows: 1 + 2 + 3 + ... + k, also written Tk = k(k+1)/2. Examples: 1, 3, 6, 10, 15. Non-example: 7 (between 6 and 10). This tutorial covers an additive loop check, a live preview, worked Python examples, edge cases, and complexity.

📝 Problem & Approach

Given a positive integer n, decide whether it equals 1+2+…+k for some k >= 1.

# 10 -> 1+2+3+4 = 10   triangular
# 7  -> between 6 and 10  not triangular
# 1  -> 1                triangular
# 6  -> 1+2+3 = 6        triangular

Inputs & Outputs

Minimal workflow

function is_triangular(num):
    if num < 1:
        return false
    total ← 0
    k ← 1
    while total < num:
        total ← total + k
        k ← k + 1
    return total = num

Method comparison

🔮 Live Preview

Adds 1, then 2, then 3… until the running total reaches or passes your target.

Press “Run check” to see the running total and the verdict.

Examples Gallery

Three complete Python programs — check 10, list triangular numbers from 1 to 50, and generate with the closed formula. Click View Output to reveal sample console results.

def is_triangular(num: int) -> bool:
    if num < 1:
        return False

    total = 0
    k = 1

    while total < num:
        total += k
        k += 1

    return total == num


number = 10

if is_triangular(number):
    print(f"{number} is a triangular number.")
else:
    print(f"{number} is not a triangular number.")

10 is a triangular number.

def is_triangular(num: int) -> bool:
    if num < 1:
        return False

    total = 0
    k = 1

    while total < num:
        total += k
        k += 1

    return total == num


print("Triangular numbers in the range 1 to 50:")
for i in range(1, 51):
    if is_triangular(i):
        print(i, end=" ")
print()

Triangular numbers in the range 1 to 50:
1 3 6 10 15 21 28 36 45

print("Triangular numbers for k = 1 to 9:")
for k in range(1, 10):
    value = k * (k + 1) // 2
    print(f"T_{k} = {k}*{k + 1}//2 = {value}")

Triangular numbers for k = 1 to 9:
T_1 = 1*2//2 = 1
T_2 = 2*3//2 = 3
T_3 = 3*4//2 = 6
T_4 = 4*5//2 = 10
T_5 = 5*6//2 = 15
T_6 = 6*7//2 = 21
T_7 = 7*8//2 = 28
T_8 = 8*9//2 = 36
T_9 = 9*10//2 = 45

🔎 Worked Walkthrough — 10 vs 7

Compare an exact hit with a miss that overshoots.

10 lands exactly; 7 is skipped between 6 and 10.

⚖️ Facts Worth Knowing

Handy follow-ups interviewers sometimes ask.

🎯 Practice Problems

Try these variations to lock in the pattern.

Notes

⏱️ Time and Space Complexity

Because T_k grows like k²/2, the additive search stops after about sqrt(2n) steps.

💡 Best Practices