作业帮lim(n→∝){1/(1*3)+1/(3*5)+...1/[(2n-1)*(2n+1)]} 求极限
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lim(n→∝){1/(1*3)+1/(3*5)+...1/[(2n-1)*(2n+1)]} 求极限
lim(n→∝){1/(1*3)+1/(3*5)+...1/[(2n-1)*(2n+1)]} 求极限
lim(n→∝){1/(1*3)+1/(3*5)+...1/[(2n-1)*(2n+1)]} 求极限
利用拆项法：数列的通项公式 1/[(2n-1)*(2n+1)] 可以拆项为 （1/2）*[1/(2n-1)-1/(2n+1)] 利用这个拆项法将极限化为 lim(n→∝){1/(1*3)+1/(3*5)+...1/[(2n-1)*(2n+1)]} = lim(n→∝)1/2{（1- 1/3)+（1/3-1/5)+...1/(2n-1)-1/(2n+1)]} = lim(n→∝)1/2{1-1/（2n+1）} = 1/2
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