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
lim(n→∝){1/(1*3)+1/(3*5)+...1/[(2n-1)*(2n+1)]} 求极限
1个回答
相关问题
-
Lim 【1/1*2+1/2*3+…+1/n(n+1)】 N→∞ 求极限
-
求极限lim [ 2^(n+1)+3^(n+1)]/2^n+3^n (n→∞)
-
求下列极限:(1)lim 3n^2-2n+1/8-n^3 n→∞ (2)lim 1+2+3+…+n/n^2 n→∞
-
求极限lim(1+2^n+3^n)^1/n.n-->无穷.
-
lim n →∞ (1^n+3^n+2^n)^1/n,求数列极限
-
求下列极限 lim n→正无穷(n^2/1+n^2/2.+n^2/n-1) lim n→正无穷[1*2/1+2*3/1+
-
求下列极限~(大一级别)1.lim(n→∞)3n^2+n+1/n^3+4n^2-12.lim(n→∞)(1/n^2+2/
-
极限计算lim2^(n+1+1/2+1/3+...+1/n)=?
-
求极限lim [1/(n+1)+1/(n+2)+...+1/(n+n)] (n→∞)
-
求1.lim(3n-(3n^2+2n)/(n-1)) 2.lim(8+1/(n+1)) 3.lim根号n(根号(n+1)