Page 189 - 'Blast_Into_Math

Blast into Math! Analatic nummer theora: ants, ghosts and giants

because for N ∈ N ,

n+N N
9 9 1

= .
10 m 10 n 10 n
m=n+1 m=1
Now we can use the Geometric Σ Theorem and the LAMP for

N
1 9
S N = , T N = S N ,
10 n 10 n
m=1
because

1/10 1 9 1 1
lim S N = = =⇒ lim T N = = .
n
N→∞ 1 − 1/10 9 N→∞ 10 9 10 n

Then,

∞
x 1 x 2 x n 9 x 1 x 2 x n 1
x = + + ... + + = + + ... + + .
10 10 2 10 n 10 m 10 10 2 10 n 10 n
m=n+1

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