这道题怎么写,有会的吗,谢谢🙏
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特例:1/5x6 = 1/5 - 1/6
规律:1/n x (n+1) = 1/n - 1/n+1
1/2x4 + 1/4x6 + ... + 1/2020x2022
= 1/2(1/1x2 + 1/2x3 + ... + 1/1010x1011)
= 1/2(1/1 -1/2 + 1/2 - 1/3 + ... + 1/1010 - 1/1011)
= 1/2(1/1 - 1/1011)
= 1/2 * 1010/1011
= 505/1011
规律:1/n x (n+1) = 1/n - 1/n+1
1/2x4 + 1/4x6 + ... + 1/2020x2022
= 1/2(1/1x2 + 1/2x3 + ... + 1/1010x1011)
= 1/2(1/1 -1/2 + 1/2 - 1/3 + ... + 1/1010 - 1/1011)
= 1/2(1/1 - 1/1011)
= 1/2 * 1010/1011
= 505/1011
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