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1964]
A PRIMER ON THE FIBONACCI SEQUENCE - PART V
65
so that
M
M
1
1
) Tan" -=r^
H.
2n+l
n=l
+ Tan" |
6
X
= 2 ^ Tan* 1 ~
+ Tan" 1
H,
-2n
^2M+2
n=l
-1
-I
-1
The limit on the left tends to Tan 1 + Tan 1/3 = Tan 2 and the right-hand
-1
side tends to this same limit and since Tan 1 / L ? M 9 -*0 9 then
Theorem 6:
I
n=l
rp
Tan
-1
1
^
T — = Tan
-1 ^ 5 " 1
1 „, ' - 1 „
—-75-— = •$ Tan
2
2n
Compare with Theorem 5 in Part IV,
We shall continue this interesting discussion in the next issue.
CORRECTIONS FOR VOLUME 1, NO. 2
Page 45: In the tenth line up from the bottom, the subscripts on the Fibonacci
numbers should be reversed.
Page 47: Replace "Lamda" by "Lambda" in the title.
Page 52: In line 6, replace (Rn) with \(R n ),
In line 12, the author's name is Jekuthiel Ginsburg.
Page 55:
In problem H-18, part a, replace = by 4= .
a b
.,, / a b
Page 57: In E2, replace — , — with , , , , , .
Page 58: Add three dots after the 4 on the last line.
Page 60: The title "Letters to the Editor" was omitted from Fibonacci Formul a s , and, in that article, the "Correct Formula" due to the late Jekuthiel
Ginsburg is I * + 2 - 3J#n + 1*_ 2 = 3 F 3 n .
66
CORRECTIONS
Feb. 1964
CORRECTIONS FOR VOLUME 1, NO. 2
Page 68: The right side of identity xix should read
I n + l " F nVl - !> •.
and in identity xx, the subscript n-1 should be n-i.
The correct page number in reference 1 is 98.
Page 75: Insert three dots after /32, in line 15.
Page 80: In the last line, replace pN by p | N and p(2 • 3 • 5- • -p ) by
p | (2 • 3 • 5 • • • p n ) .
Page 81: Replace T + 1 by T
in the left side of the first displayed
equation.
Page 86: In B-12, L
= fa
], a34 = i = \T-l
instead of zero.
Page 87: Change the equations in problem B-16 to read
F2
F
F
n-1
n-1 n
Rn = 2 F - F
F2
- F nF
1
n-1 n
n+1
n-1 n
F2
F F
n
n n+1
See also solution in this issue.
Page 88:
F2
n
2F F x 1
n n+1
F2
n+1
See the last written line for notational error due to exclamation
point punctuation.