Swiss Micros DM42 and TI-84 Plus: Sum of an Infinite Geometric Series
Introduction
An infinite geometric series has the form:
a + a × r + a × r^2 + a × r^3 + ...
= a × (1 + r + r^2 + r^3 + ....)
If |r| < 1, the series converges and a sum exists.
∞
Σ a × r^n = a ÷ (1 - r)
n=0
∞
Σ a × r^(n-1) = a ÷ (1 - r)
n=1
However if |r| ≥ 1, the series diverges and does not have as sum.
DM42 Program: GSUM
Calculators: DM42, HP 42S, Free42, Plus42
00 { 36-Byte Prgm }
01▸LBL "GSUM"
02 ENTER
03 ABS
04 1
05 X<>Y
06 X>Y?
07 GTO 00
08 R↓
09 R↓
10 1
11 X<>Y
12 -
13 ÷
14 RTN
15▸LBL 00
16 CLX
17 "DIVERGES"
18 AVIEW
19 .END.
In the case the series diverges, the X stack is cleared (displays 0).
TI-84 Plus Program: GSUM
Calculators: TI-84 Plus, TI-84 Plus CE (Python), TI-83 Premium CE (Python)
Disp "Σ(A*R^N,0,INF)","Σ(A*R^(N-1),1,I)"
Prompt A,R
ClrHome
Disp "A=",A,"R=",R
If abs(R)<1
Then
A/(1-R)→S
Disp "SUM=",S
Else
Disp "DIVERGES"
End
Examples
A: 3, R: -0.2
Stack: Y = 3, X = -0.2
Result = 2.5
A: 3, R: 0.2
Stack: Y = 3, X = -0.2
Result = 3.75
A: 3, R: -2.2
Stack: Y = 3, X = -2.2
Result = diverges
A: 3, R: 2.2
Stack: Y = 3, X = 2.2
Result = diverges
Eddie
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