求下列幂级数的和函数
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利用e^x=1 + x/1! + x^2/2! +... + x^n/n!+... = sum(x^n/n!)求
n^2 +1 = n^2 -n +n +1
s1(x)= sum(x^n/3^n n!) = e^(x/3)
s2(x)= sum(nx^n/3^n n!) = x/3 * sum( x^(n-1)/3^(n-1) *(n-1)!) =x/3 * e^(x/3)
s3(x)=sum(n(n-1)x^n/3^n n!) = x^2/9 sum(x^(n-2)/3^(n-2) (n-2)!) = x^2/9 e^(x/3)
所以和函数为(1+x/3+x^2/9)e^(x/3)
n^2 +1 = n^2 -n +n +1
s1(x)= sum(x^n/3^n n!) = e^(x/3)
s2(x)= sum(nx^n/3^n n!) = x/3 * sum( x^(n-1)/3^(n-1) *(n-1)!) =x/3 * e^(x/3)
s3(x)=sum(n(n-1)x^n/3^n n!) = x^2/9 sum(x^(n-2)/3^(n-2) (n-2)!) = x^2/9 e^(x/3)
所以和函数为(1+x/3+x^2/9)e^(x/3)
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