1/3^2-1+1/5^2-1+1/7^2-1``````+1/(2N+1)^2-1+````= 答案:A1/4 B1 C1/2 D无法计算
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解决时间 2021-02-18 04:30
- 提问者网友：暗中人
- 2021-02-17 22:33
1/3^2-1+1/5^2-1+1/7^2-1``````+1/(2N+1)^2-1+````= 答案:A1/4 B1 C1/2 D无法计算
最佳答案
- 五星知识达人网友：煞尾
- 2021-02-17 22:58
1/3^2-1+1/5^2-1+1/7^2-1``````+1/(2N+1)^2-1+````
=1/(3+1)(3-1)+1/(5+1)(5-1)+1/(7+1)(7-1)+...+1/(2N+1+1)(2N+1-1)+...
=1/4*2+1/6*4+1/8*6+...+1/(2N+2)2N
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2N-1/(2N+2))
=1/2(1/2-1/(2N+2))
=1/4-1/(4N+4)
当N趋于无穷大时
原式=1/4
故选A
=1/(3+1)(3-1)+1/(5+1)(5-1)+1/(7+1)(7-1)+...+1/(2N+1+1)(2N+1-1)+...
=1/4*2+1/6*4+1/8*6+...+1/(2N+2)2N
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2N-1/(2N+2))
=1/2(1/2-1/(2N+2))
=1/4-1/(4N+4)
当N趋于无穷大时
原式=1/4
故选A
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