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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 11
# Folio 7r, page id 00068082:0013
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 29. Junij 167C
i
+X aequ.
FX Cae
De ex pressione potestatum
et summis reciphocorum
+ im AX + M - 1. B
sive
CX
2
X + m- 2
+ M =  m + 12 M ∞ 1,2, 3 M
1
+ 113
1, 2, 39
+2,3
Cx et
D.
absolvendo multis licationem: servint haec
l1+X aequ. 1 + m X + M - , M X + m - 1m + 1, 2m X3
1, 2,3
series ad summas
hujus modi sericium
timrationalium reci–
procarum, quam irra
tionalium in numeris
veniendas.
4 m = 1M + 1Z n 1, 23m
14
2
3
1724 4 173, 2M
112,4
214 273,7
patet quemlibet Terminum fieri ex ducta continuorum in se invicem. 
tel
m 1+X aequ. 1+
12,3,4,5
_,mX + B. m m-1 V
+ _, m m- 1, m- 2, m.3,  4
1,2
C
X
Videamus quid frat si valor inventus ordinetur
fiet:
1+ X m
e
+1 X m
= 1-2 1
Cr
LMomM -1, M - 2
172,3
13
secundum M. Scilicet
si m sit 1 debent destrui omnia peleter duos pri–
mos terminos 1 et X n seu 14 X. Hinc sequitur
MHO et + 12 1t2
 11
destruuntur ultra tres priores terminos
Valdenotabilis reductio
sunt ergo summae ex ductis an natura
libus in triangulare;ac per
consequens etiam summabires
invenori possunt hae summae
sunt ergo summae ex ductis prae
cedentibus (id est summis ex naturatibis
in triangulares duc) in naturales
s
 1+
2
Eodem modo: 12
2
3
2l, + 3,3, +4
172, 4
+13,4
213
6, 17 (3, 12, +2
11, 2
,3
e
yt3