t
1
1
1
a(0) =1.
t
1
k > 0
k t
A(t) = k · a(t),
a(t)
a(0) = 1 A(0) = k
A(t)
In n
In = A(n) - A(n - 1)
n 1
A(t)
1
" A(t) = t + k
2
" A(t) = exp{2t} + k
" A(t) = k
"
i
1
i = a(1) - a(0)
a(1) = 1 + i.
1
8% 0, 08
(1 + i) - 1 a(1) - a(0) A(1) - A(0) I1
i = = = = .
1 a(0) A(0) A(0)
n in
A(n) - A(n - 1) In
in = =
A(n - 1) A(n - 1)
n
1
a(t) = 1 + it
t 0
a(n) - a(n - 1) [1 + in] - [1 + i(n - 1)] i
in = = =
a(n - 1) 1 + i(n - 1) 1 + i(n - 1)
n 1 in
n
1 Ò! 1 · (1 + i) Ò! (1 + i) · (1 + i) Ò! (1 + i)2 · (1 + i) Ò! . . .
a(t) = (1 + i)t
t 0
a(n) - a(n - 1) (1 + i)n - (1 + i)n-1 (1 + i) - 1
in = = = = i
a(n - 1) (1 + i)n-1 1
n 1 in n
1 1
k
1 = (1 + i) · k.
1
k = .
1 + i
1
1 = (1 + i)2 · k
2
1 1
k = = .
(1 + i)2 1 + i
n 1
n
1 1
k = = .
(1 + i)n 1 + i
a(n) = (1+i)n
1 1
k = = = a-1(n).
(1 + i)n a(n)
1 1
k = = = a-1(n).
1 + in a(n)
1
v = .
1 + i
1 + i
v(t) = a-1(t)
1
a-1(t) = ,
1 + it
1
a-1(t) = = vt.
(1 + i)t