Question

1 and 8 are the first two natural numbers for which 1 + 2 + 3 + ...... + n is a perfect square. which number is the 4th such number?​

Answer 1

Answer:

The 4th such number is 288.

Step-by-step explanation:

Did a computer search in Python and got:

• 1  =  1×2/2 =  1×1  =  1²
• 1 + 2 + … + 8  =  8×9/2  =  4×9  =  2²×3²  =  6²
• 1 + 2 + … + 49  =  49×50/2  =  49×25  =  7²×5²  =  35²
• 1 + 2 + … + 288  =  288×289/2  =  144×289  =  12²×17²  =  204²

So the first 4 such numbers are 1, 8, 49, 288.

Hope that helps.