Show that :
The sum 1+9+9^2+9^3+9^4...+9^k is always a triangular number
This is a finite geometric series with sum = XXXXX which is triangular.
You got it!
Anyway there 100`s ways to compute the sum of consecutive integers (1,2,3,....n)
I will post them one day with the method on how to find such closed formulas.
1+9+92+⋯+9k1+9+92+⋯+9k is a triangular number for all kk.
However all triangular numbers are not of this form.