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常用级数

11x=1+x+x2+x3+x4+=1+k=1xk

(1+x)α=1+k=1(αk)xk, (αk)=α(α1)(αk+1)k!

ex=1+x+x22!+x33!+x44!+=1+k=1xkk!

ln(1+x)=xx22+x33x44+x55=k=1(1)k1xkk

cosx=1x22!+x44!x66!+x88!=1+k=1(1)kx2k(2k)!

sinx=xx33!+x55!x77!+x99!=k=1(1)(k1)x2k1(2k1)!

arctanx=xx33+x55x77+x99=k=1(1)k1x2k12k1

1(1x)k=n=0(n+k1k1)xn