常用级数¶ 11−x=1+x+x2+x3+x4+⋯=1+∑k=1∞xk (1+x)α=1+∑k=1∞(αk)xk, (αk)=α(α−1)⋯(α−k+1)k! ex=1+x+x22!+x33!+x44!+⋯=1+∑k=1∞xkk! ln(1+x)=x−x22+x33−x44+x55−⋯=∑k=1∞(−1)k−1xkk cosx=1−x22!+x44!−x66!+x88!−⋯=1+∑k=1∞(−1)kx2k(2k)! sinx=x−x33!+x55!−x77!+x99!−⋯=∑k=1∞(−1)(k−1)x2k−1(2k−1)! arctanx=x−x33+x55−x77+x99−⋯=∑k=1∞(−1)k−1x2k−12k−1 1(1−x)k=∑n=0∞(n+k−1k−1)xn