函数f(x)=ex/2T在x=0处的泰勒级数为____．

函数f(x)=ex/2T在x=0处的泰勒级数为____．
【正确答案】：∑n=0∞xn/(2n•n!’)-∞﹤x﹤+∞。解析：由于ex=∑n=0∞xn/n!’-∞﹤x﹤+∞以x/2代入得ex/2=∑n=0∞(x/2)n/n!=∑n=0∞xn/(2n•n!’)-∞﹤x﹤+∞