The units digit of a triangular number iw ## 0, 1, 3, 5, 6 ##?

[Math100]

Homework Statement

Prove the following statement:
The units digit of a triangular number is $0, 1, 3, 5, 6$, or $8$.

Relevant Equations

None.

Proof:

Let $t_{n}$ denote the $nth$ triangular number such that $t_{n}=\frac{n^{2}+n}{2}$ for $n\geq 1$.
Then $n\equiv 0, 1, 2, 3, 4, 5, 6, 7, 8$, or $9\pmod {10}$.
Thus $t_{n}\equiv 0, 1, 3, 6, 10, 15, 21, 28, 36$, or $45\pmod {10}$.
Therefore, the units digit of a triangular number is $0, 1, 3, 5, 6$, or $8$.

 

[fresh_42]

Homework Statement:: Prove the following statement:
The units digit of a triangular number is $0, 1, 3, 5, 6$, or $8$.
Relevant Equations:: None.

Proof:

Let $t_{n}$ denote the $nth$ triangular number such that $t_{n}=\frac{n^{2}+n}{2}$ for $n\geq 1$.
Then $n\equiv 0, 1, 2, 3, 4, 5, 6, 7, 8$, or $9\pmod {10}$.
Thus $t_{n}\equiv 0, 1, 3, 6, 10, 15, 21, 28, 36$, or $45\pmod {10}$.
Therefore, the units digit of a triangular number is $0, 1, 3, 5, 6$, or $8$.

Right. I think it is time to proceed to the next paragraph now, something more challenging.