higher algebra a sequel to elementary algebra for schools

8/19/2019 Higher Algebra a Sequel to Elementary Algebra for Schools
http://slidepdf.com/reader/full/higher-algebra-a-sequel-to-elementary-algebra-for-schools 1/585
of
r
the
expression
nGr
is
greatest
un
the
reciprocal
f
the
product
of
n
factors
in
A.
P
316
Method
of
Subtraction
318
Expression
of
un
as
sum
J'2
l) (fc2
(a
13.
If
an
equation
is
homogeneous
with
respect
by
.r,
X2
?/2
s2
prove
that
example,
of
1
is
nearly
falling
if
a
body
falls
through
402^
feet
in
5
seconds,
;
Art.
43,
the
terms
thus
inserted
are
Example
1.
The
sum
term
is
is
equal
to
the
sum
of
the
first
two
terms
of
the
firstseries.
;
LAlt-bb-
(4)J'
layer
is
n
base.
2.
A
triangularile,
aving
18
of its
a
triangularpile
is
to
by
r
5.
Express
5381
in
powers
of
nine.
6.
Transform
212231
eight.
11.
Transform
400803
from
the
nonary
to
the
quinary
scale.
12.
Express
the
septenary
number
20665152
in
powers
of
12.
13.
Transform
ttteee
from
scale
twelve
to
the
common
scale.
3
14.
Express
24.
Find the radix of the scale in which the numbers denoted
by
479,698,
907
are
in
arithmetical
progression.
25.
In
what
scale
are
21.
G
24.
use
of
imaginary
quantities
here
is
one
point
of
importance
which
;
a-x f-i
2-5\/rl
31.
If
ax +
cy
equal
ratios
and
equate
it
to
the
product
of
ax2
equation
(3)
is
homogeneous.
The
a
valuable
artifice.
\x-yj
\.v
(5).
Hence
from
(4)
and
(5),
by
division
y-*-3.
from
each
side,
and
we
obtain
nPr
may
be
are
rest,
x
product
xn~
in
n
things
2
at
a
time
n
applied
o
expand
expressions
hich
contain
more
than
two
terms.
in
the
case
of
negative
and
fractional
is
any
negative
uantity.
It
r
up
to
37,
we
have
xr
+
the
first
few
terms
20.
If
a0,
a15
a2
ft3
are
the
coefficients
in
order
Example.
log
42
logarithms
f
integers.
This
proposition
e
proceed
to
prove.
213.
any
logarithm
has
been
taken
KM) *a-K+t)
]3+\i
2).
l) *-
Logar-thms
may
one
year,
n
PR3,
and
a sum
of money
may
often
be
more
simply
effected
by
the
quantities
a,
b,c,...k
re
equal.
{1
u)
^-i)
%1;
'u
quantity
to
discuss
some
propositions
connected
with
the
limiting
..
'
x -a
(2).
From
(1)
yet greater
than X.

=
equation
1
un+i
(log
a)'
np'
The
constant
factor
7=
r_
is
common
to
every
term
3
3.6
2
3.6.9
+
=
+pH,
qoxn
instance,
f
p0x
each
of
the
coefficients
an
a.,,
a0
is
equal
to
zero
identically.
H.
ir.A.
17
n-2)*+1-
(-l)w
\n;
;
. .
1
the last article
general
term
is
quotients
0
a0,
1
to
find
a
convergent
of
the
convergent.
investigation
equation
ax
limited,
integer
in
C
C
r
readily
found.
=
-
of
n;
we
thus
obtain
=
ai:c,+%
ay;
here
cn
-bn-bu
u
so
that
cn
is
of
p
(1 ax)(1
we
have
obtained
a
Example
4.
A2{nr'1-(n-iy-1}
the
advanced
student
may
consult
Boole's
Finite
Differences.
Example.
Find
the
(n-r+^-1),
no
common
factor
except
unity
are
said
term
of
the
product
8064.
7.
In
how
3?i
or
431.
To
find
the
number
_++_+..._
.
. .
+
+
....
proved
without
using
the
result
quoted
from
Art.
314,
as
-
of
(H-a?)*-*
re
alternately
reater
and
less

nth
con-ergent
useful.
12
3
Example.
2- 3- 4-
2(e2-l)
1+
2+
3+
n+
\aj
axaj
a0
a0(a1-
Vi)
a0x
o+
a1
happening
is
representedy
ka,
where
extreme
coins
being
to
happens
drawing
a
sovereign
s
is
a
multiple
the
first
to
in-
n
troduce
the
following
efinition
case
of
success,
the
sum
of
money
denoted
by
pM
sum
^
causes.
472,
we
agree
in
telling
he
same
falsehood
the
quantity
becomes
smaller
as
the
number
of
not
is
the
onlysovereign
shilling
ith
are
red.
8.
A
purse
contains
five
coins,
same
purse;
and
(2)
correct.
19.
Ten
witnesses,
ach
of
whom
statement,
even
although
the
a
'priori
probability
Place
n
ways
6
or
5.
a or
39
13
81
24
21
14
26
We
have
67
39
81
10
by
twice
the
corresponding
constituents
determinants
that
remain
are
equal
to
(a
Ay3
can
be
obtained
from
it
by
suitable
interchanges
f
suffixes
and
adjustment
of
signs.
[Elementary
lgebra,
Arts.
21,
22]
not
involve
x
P-^ 3+
x,
we
have
ty+z)*(e+x)*(x+y)*=tx*(y+zY+2(^z)3-2^2z*'
22.
by
\z
y)
\x
z)
\y
x)
+Pn-lX
not
the
case
=
http://slidepdf.com/reader/full/higher-alge

higher algebra a sequel to elementary algebra for schools

Documents