求极限lim(n趋近无穷){1/(n^2+1)+2/(n^2+1)+...+2n/(n^2+1)}
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求极限lim(n趋近无穷){1/(n^2+1)+2/(n^2+1)+...+2n/(n^2+1)}求极限lim(n趋近无穷){1/(n^2+1)+2/(n^2+1)+...+2n/(n^2+1)}求极
求极限lim(n趋近无穷){1/(n^2+1)+2/(n^2+1)+...+2n/(n^2+1)}
求极限lim(n趋近无穷){1/(n^2+1)+2/(n^2+1)+...+2n/(n^2+1)}
求极限lim(n趋近无穷){1/(n^2+1)+2/(n^2+1)+...+2n/(n^2+1)}
1/(n^2+1)+2/(n^2+1)+...+2n/(n^2+1)
=(1+2+3+...+2n)/(n^2+1)
=(1+2n)n/(n^2+1)
=(2n^2+n)/(n^2+1)
lim(n趋近无穷){1/(n^2+1)+2/(n^2+1)+...+2n/(n^2+1)}
=lim(n趋近无穷) (2n^2+n)/(n^2+1) (上下同除以n^2)
=lim(n趋近无穷) (2+1/n)/(1+1/n^2)
=2
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