**TI-60: Triangle Numbers**

**Introduction**

The following program calculates T_n, the nth triangle number. Triangle numbers are determined by the sum:

T_n = ∑k, from k = 0 to n

The TI-60 does not have either comparison commands or a goto command. Luckily for the TI-60 (not the case for the TI-55 III), the RST sends the program pointer back to the first step (Step 00) and continues to execute.

We simulate a loop by counting down, when the counter reaches -1, the square root function will cause an error, forcing execution to stop. You’ll see this trick towards the end of the program.

Instructions:

1. In RUN mode (outside of LRN), store the following values:

R0 = 0

R1 = n

2. Execute the program by pressing [RST], [R/S]. The program is done when you see “Error”.

3. Clear the error by pressing [CE/C].

4. Recall R0. This is your triangle number. (R1 will have -1).

**TI-60 Program: Triangle Numbers**

PC00 OP71: RCL

PC01 OP01: 1

PC02 OP61: STO

PC03 OP85: +

PC04 OP00: 0 // sum R1 in R0

PC05 OP75: –

PC06 OP01: 1

PC07 OP95: =

PC08 OP61: STO

PC09 OP01: 1 // store R1 -1 in R1

PC10 OP86: √ // square root of R1, if less than 0, program stops

PC11 OP22: RST // reset back to step 00

Examples:

T_5 = 15 (0 [STO] 0, 5 [ST0] 1, [RST] [R/S], [CE/C] [RCL] 0)

T_35 = 630 (in about 45 seconds)

Eddie

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