求幂级数 ∑(∞,n→0)(2n+1)x^n的收敛域及和函数.
求幂级数 ∑(∞,n→0)(2n+1)x^n的收敛域及和函数.
数学人气:902 ℃时间:2020-03-07 13:10:07
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∑(∞,n→0)(2n+1)x^nR=lim|2n-1/2n+1|=1x=1时∑(∞,n→0)(2n+1)发散,x=-1时∑(∞,n→0)(-1)^n(2n+1)也发散,所以收敛域为(-1,1)令s(x)=∑(∞,n→0)(2n+1)x^n=∑(∞,n→1)2nx^n+∑(∞,n→0)x^n再令∑(...
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