1 n
m
sn|(1 + i)m = sn+m| - sm|.
sn|(1 + i)m-1 = sn+m-1| - sm-1|.
¨ ¨ ¨
n
m (m an|(1 + i)m = vn-msn| = sm| + an-m|
a"| = v + v2 + v3 + . . . =
v
= =
1 - v
v
= =
iv
1
= .
i
1 - vn 1
a"| = lim an| = lim =
n" n"
i i
lim vn = 0.
n"
1
ä"| = .
d
a(t)
v(t) = a-1(t)
n
1
an| = .
a(t)
t=1
n n
a(n) 1
sn| = = a(n) .
a(t) a(t)
t=1 t=1
n
n
n-1
sn| = 1 + (1 + i) + (1 + 2i) + . . . + [1 + (n - 1)i] = a(t)
t=0
n-1 n-1
a(t) 1
an| = = a(t).
a(n) a(n)
t=0 t=0
k
k
i n n
n k
n/k
1 k
n vk - vn+k
·k
k
vk + v2k + . . . + v = =
1 - vk
1 - vn
= =
(1 + i)k - 1
an|
= .
sk|
an| sn|
(1 + i)n = .
sk| sk|
" R
n
" 1 k
n 1
n/k
Ran|.
R
1
Rsk| = 1.
R = 1/sk|
1 - vn
1 + vk + v2k + . . . + vn-k = =
1 - vk
an|
= .
ak|
an| sn|
(1 + i)n = .
ak| ak|
vk
vk + v2k + . . . = =
1 - vk
1
= =
(1 + i)k - 1
1
=
isk|
1
.
iak|
m
n
i
m n
mn
1/m
1
1 1 2 1
m m m
a(m) = v + v + . . . + vn- + vn
n|
m
îÅ‚ Å‚Å‚
1 1
m m
1 v - vn+
ðÅ‚ ûÅ‚
=
1
m m
1 - v
1 - vn
=
1
m
m (1 + i) - 1
1 - vn
= .
i(m)
s(m) = a(m)(1 + i)n
n| n|
(1 + i)n - 1
= .
i(m)
i i(m)
an| a(m) sn| s(m)
n| n|
i
a(m) = an|
n|
i(m)
i
s(m) = sn|.
n|
i(m)
i
s(m)
i(m) 1|
1/m
1 - vn
ä(m) = .
n|
d(m)
s(m) = ä(m)(1 + i)n
¨n|
n|
(1 + i)n - 1
= .
d(m)
i
ä(m) = an|
n|
d(m)
i
s(m) = sn|.
¨n|
d(m)
i
s(m)
¨1|
d(m)
ä(m) an| s(m) sn|
¨n|
n|
1
m
ä(m) = (1 + i) a(m)
n| n|
i(m) i
= 1 + an|
m i(m)
i i
= + an|
i(m) m
i i
s(m) = + sn|.
¨n|
i(m) m
1
a(m) =
"|
i(m)
1
ä(m) = .
"|
d(m)
m
"
n
1 1
n


n| = vtdt.
0
n


n| = vtdt
0
vt n
=
ln v
0
1 - vn
= .
´
1 - vn 1 - vn


n| = lim a(m) = lim =
n|
m" m"
i(m) ´
1 - vn 1 - vn


n| = lim ä(m) = lim = .
n|
m" m"
d(m) ´
lim d(m) = lim i(m) = ´.
m" m"


n| an|
i


n| = an| = s1|an|.
Å»
´
n
sn| = (1 + i)tdt
Å»
0
(1 + i)t n
=
ln(1 + i)
0
(1 + i)n - 1
=
´
i
= sn| = s1|sn|
Å»
´
= lim s(m) = lim s(m).
¨n|
n|
m" m"
n n t
d
st| = (1 + i)t
Å»
dt
= 1 + ´st|.
Å»
d


t| = vt
dt
= 1 - ´

t|.
´
1 - e-n´


n| =
´
en´ - 1
sn| = .
Å»
´