∑[n:1→∞]x^n /4^n =∑[n:1→∞](x/4)^n
显然，当-1
部分和Sn=(x/4)[1-(x/4)^n] /(1- x/4)
=x[1-(x/4)^n] /(4-x)
故和函数S=lim[n→+∞]Sn
=lim[n→+∞]x[1-(x/4)^n] /(4-x)
=x(1-0)/(4-x)
=x/(4-x)
隔项级数。得收敛半径的平方
R^2 = lim
= lim
∑
= [∑
= {x^2[e^(x^2)-1]}' = [x^2e^(x^2)-x^2]'
= 2xe^(x^2)+ 2x^3e^(x^2)-2x = 2x(1+x^2)e^(x^2) - 2x
(-∞ < x < +∞)
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