403
правки
Изменения
м
→y = ln(x + 1)
<tex>y^{(k + 1)}(x) = [(1 + x)^{-1}]^{(k)} = (-1)\ldots(-1 - k + 1)(x + 1)^{-1-k}</tex>
<tex>\left. y^{(k + 1)}(0) = (-1)\ldots(-1 - k + 1)(x + 1)^{-1-k} \right|_0 = (-1)(-1 -1)\ldots(-k) = (-1)k^kk!</tex>
<tex>y = \ln(x + 1) = \sum\limits_{k = 1}^n (-1)^k\frac1k x^k + o(x^n)</tex>
