幂级数∑(1~∞)x^(2n-2)/(2n-2)!是如何变换到∑(0~∞)x^(2n)/(2n)!

Question

幂级数∑(1~∞)x^(2n-2)/(2n-2)!是如何变换到∑(0~∞)x^(2n)/(2n)!

Answer 1

令 k=n-1 ,n=k+1当n=1,2,3 .时
k=0,1,2.
所以 ∑(1~∞)x^(2n-2)/(2n-2)!
=∑(0~∞)x^(2(k+1)-2)/(2(k+1)-2)!
=∑(0~∞)x^(2k)/(2k)!
=∑(0~∞)x^(2n)/(2n)!
无非是第一个级数从1开始加,第二个从0还始加