Заполните таблицу значений выражения (-1)^(m+1)*1/(m+1)-m/(m-1) при m∈Z; -1<m<=4.

Ответ:

\[( - 1)^{m + 1} \cdot \frac{1}{m + 1} - \frac{m}{m - 1} =\]

\[= \frac{( - 1)^{m + 1}}{m + 1} - \frac{m}{m - 1}\]

\[m = 0:\]

\[\frac{1}{1} - \frac{0}{- 1} = 1.\]

\[m = 1:\]

\[\frac{1}{2} - \frac{1}{0} - не\ имеет\ смысла.\]

\[m = 2:\]

\[- \frac{1}{3} - \frac{2}{1} = - \frac{1}{3} - 2 = - 2\frac{1}{3}.\]

\[m = 3:\]

\[\frac{1}{4} - \frac{3}{2} = \frac{1}{4} - 1\frac{1}{2} = \frac{1}{4} - 1\frac{2}{4} = - 1\frac{1}{4}.\]

\[m = 4:\]

\[- \frac{1}{5} - \frac{4}{3} = - \frac{1}{5} - 1\frac{1}{3} =\]

\[= - \frac{3}{15} - 1\frac{5}{15} = - 1\frac{8}{15}.\]