Cool math with the number 2025 for the new year!

[stickfiftyfive]

Also, 2025 is among the first few elements in this self-referencing iterated sequence, via Domotro from Combo Class.

Where T(n) is a triangular number,
and with n > 1:
T(2) = 3
3^2 = 9
T(9) = 45
45^2 = 2, 025
T(2, 025) = 2, 051, 325
2, 051, 325^2 = 4, 207, 934, 255, 625
T(4, 207, 934, 255, 625) = 8, 853, 355, 349, 833, 265, 389, 198, 125
Tn^2 = 78, 381, 900, 950, 421, 300, 982, 881, 904, 787, 876, 752, 731, 430, 503, 515, 625

k = sum of first n cubes
n = 2, k = 9
n = 9, k = 2, 025
n = 2, 025, k = 4, 207, 934, 255, 625
k = 78, 381, 900, 950, 421, 300, 982, 881, 904, 787, 876, 752, 731, 430, 503, 515, 625

[stickfiftyfive]

Also, since no one else has stated it:
The sum of the first n cubes, where n is a postive integer, is always equal to the n-th triangular number squared, and 45 is the 9th triangular number.

[lenartszabi]

My math teacher just sent it to our class groupchat 😂

[therainbowwillow]

This is super cool! (Loved the factorial joke too lol)

[Geography]

That was because 9-1 and everything in between added is 45

[gabrielk]

2025 divided by some specific number, gives me the distance from my home to all Mc Donalds.

[jimmy]

If you take the number 2026 and subtract one, it's also 2025!!! 😮 Must be aliens!!