Folios 31-32: ADM to AAL
[31r] My dear Lady Lovelace
You are right about
the writing down of the
terms:
\(\frac{z}{(2n-2)(2n-3)}\)
is the \(n\) th term divided
by the \((n-1)\) th and the
\( \overline{n+1}\) th divided by the
\( n\) th is \(\frac{z}{2n(2n-1)}\) as you
make it.
If I understand you correctly
[31v] you are now satisfied about
all the rest
Suppose you try at what
term convergency begins in the
following series
\(1+\frac{x}{2.4}+\frac{x^2}{2.4.6.8}+\frac{x^3}{2.4.6.8.10.12}\)
\(+\cdots\cdots\)
when \(x=100,000\)
With remembrances to
Lord Lovelace
I remain
Yours truly
ADeMorgan
69 G.S.
Thursday
[32r] You will see the alteration
I have made in your paper
If you do not see it
clearly, write again for
the sort of point con-
tained in it is one
of importance.
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