TI 84 Plus CE: Nested Square Root Sums
Introduction
The program NESTSQM calculates the sequence:
√(a + b)
√(a + b * √(a + b))
√(a + b * √(a + b * √(a + b))
√(a + b * √(a + b * √(a + b * √(a + b)))
...
√(a + b * √(a + b * ... * √(a + b)))
In other words, start with c = 1.
Then let c = √(a + b * c)
Repeat.
The calculation is shown in steps of 5, for a total of 25 steps.
TI-84 Plus CE Program: NESTSQSM
"2020-01-05 EWS"
Disp "√(A+B√(A+B√(A+B...","25 ITERATIONS","TI-84+ CE"
Prompt A,B
1→C
For(K,1,25)
√(A+B*C)→C
Disp C
If fPart(K/5)=0
Then
Disp " "
Disp toString(K-4)+" TO "+toString(K)
Pause
ClrHome
End
End
Examples
Example 1: a = 2, b = 3
2.236067977
2.95096661
3.294373966
3.447190436
3.513057259
3.541069299
3.552915408
3.557913184
3.5600196
3.560907019
3.561280817
3.561438256
3.561504565
3.561532493
3.561544255
3.561549208
3.561551295
3.561552173
3.561552544
3.561552699
3.561552765
3.561552793
3.561552804
3.561552809
3.561552811
Example 2: a = 7, b = 4
3.31662479
4.501832867
5.000733093
5.196434583
5.271217917
5.299516173
5.310184996
5.314201726
5.315713207
5.316281861
5.316495786
5.316576262
5.316606535
5.316617923
5.316622207
5.316623819
5.316624425
5.316624653
5.316624739
5.316624771
5.316624783
5.316624788
5.316624789
5.31662479
5.31662479
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
Introduction
The program NESTSQM calculates the sequence:
√(a + b)
√(a + b * √(a + b))
√(a + b * √(a + b * √(a + b))
√(a + b * √(a + b * √(a + b * √(a + b)))
...
√(a + b * √(a + b * ... * √(a + b)))
In other words, start with c = 1.
Then let c = √(a + b * c)
Repeat.
The calculation is shown in steps of 5, for a total of 25 steps.
TI-84 Plus CE Program: NESTSQSM
"2020-01-05 EWS"
Disp "√(A+B√(A+B√(A+B...","25 ITERATIONS","TI-84+ CE"
Prompt A,B
1→C
For(K,1,25)
√(A+B*C)→C
Disp C
If fPart(K/5)=0
Then
Disp " "
Disp toString(K-4)+" TO "+toString(K)
Pause
ClrHome
End
End
Examples
Example 1: a = 2, b = 3
2.236067977
2.95096661
3.294373966
3.447190436
3.513057259
3.541069299
3.552915408
3.557913184
3.5600196
3.560907019
3.561280817
3.561438256
3.561504565
3.561532493
3.561544255
3.561549208
3.561551295
3.561552173
3.561552544
3.561552699
3.561552765
3.561552793
3.561552804
3.561552809
3.561552811
Example 2: a = 7, b = 4
3.31662479
4.501832867
5.000733093
5.196434583
5.271217917
5.299516173
5.310184996
5.314201726
5.315713207
5.316281861
5.316495786
5.316576262
5.316606535
5.316617923
5.316622207
5.316623819
5.316624425
5.316624653
5.316624739
5.316624771
5.316624783
5.316624788
5.316624789
5.31662479
5.31662479
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.