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【OG20-P153-50题】
If S=1+122 +132 +142 +152 +162 +172 +182 +192 +1102 ,which of the following is true?
分析A选项
分析B选项
分析C选项
分析D选项
分析E选项
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S = 1 + 1/2²+ 1/3²+ 1/4²+ 1/5²+ 1/6²+ 1/5²+ 1/8²+ 1/9²+ 1/10²
1/2²>1/3²>1/4²>1/5²>1/6²>1/5²>1/8²>1/9²>1/10²S < 1 + 1/2²+ 1/2²+ 1/4²+ 1/4²+ 1/4²+ 1/4²+ 1/8²+ 1/8²+ 1/8²
S < 1 + 1/2²*2+ 1/4²*4+ 1/8²*3
S < 1 + 1/4+ 1/4+ 3/64<2
S<2
226058gxkp
1/n^2 <1/(n(n-1))=1/(n-1)-1/n 1/n^2数列和 收敛数列 趋向于0
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2022-09-13 20:39:33
司令Selin
S = 1 + 1/2²+ 1/3²+ 1/4²+ 1/5²+ 1/6²+ 1/5²+ 1/8²+ 1/9²+ 1/10² 1/2²>1/3²>1/4²>1/5²>1/6²>1/5²>1/8²>1/9²>1/10² S < 1 + 1/2²+ 1/2²+ 1/4²+ 1/4²+ 1/4²+ 1/4²+ 1/8²+ 1/8²+ 1/8² S < 1 + 1/2²*2+ 1/4²*4+ 1/8²*3 S < 1 + 1/4+ 1/4+ 3/64<2 S<2
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2022-07-16 00:48:35
cchloee
这一题的话可以这么做。 排除A，B， S>3 S=3 太大了不可能发生 S=1+1/（3^2） * 9 ， 1／3^2 是大于所有的数字的除了1/4^2， 所以说这个S是Max， 结果=2， 所以S只有可能小于2
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2021-06-28 06:35:19
587594pfxh回复cchloee
你怎么证明S＜1+1/（3^2）*9一定成立啊？还有个1/（2^2）呀
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2023-05-17 11:25:48
1259969exa
1/n^2 <1/(n(n-1))=1/(n-1)-1/n 通过这个关系式我们可以知道一个数的平方的倒数一定是小于它前面的一个数的倒数减去它本身的倒数的。通过这个式子可以化简上面的式子为： S<1+（1/1-1/2)+(1/2-1/3)+(1/3-1/4)......(1/9-1/10)<2-1/10.所以得到S<2。
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2021-04-06 16:04:10
keyi
1/n^2数列和的极限为pi^2/6 < 2
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2021-03-28 19:54:55
186956skjmq
1/n^2 <1/(n(n-1))=1/(n-1)-1/n 通过这个关系式我们可以知道一个数的平方的倒数一定是小于它前面的一个数的倒数减去它本身的倒数的。通过这个式子可以化简上面的式子为： S<1+（1/1-1/2)+(1/2-1/3)+(1/3-1/4)......(1/9-1/10)<2-1/10.所以得到S<2。
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2020-09-25 02:13:27
vitamint1230回复186956skjmq
不对吧
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2020-10-20 17:44:48
什么彤同学回复 186956skjmq
正解
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2021-01-04 23:04:23
吃700的鸡
1/2*2＜1/1*2，1/3*3＜1/2*3，1/4*4＜1/3*4，以此类推 所以原式＜1+1/1*2+1/2*3+1/3*4＋....＋1/9*10 右边=1+1-1/2+1/2-1/3＋....+1/9-1/10=2-1/10＜2 所以原式也小于2
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2020-02-11 23:03:28
1289311ww
Now, let's convert a few of the fractions to decimal approximations... S = 1 + 0.25 + 0.11 + 0.06 + 0.04 + . . . Add the first 4 values.... S = 1.42 + 0.04 + . . . IMPORTANT: Notice that each fraction is less than the fraction before it So, all of the 5 decimals after 0.04 will be less than 0.04 So, if we replace all of those 5 decimals with 0.04, our new sum will be greater than the original sum So: S < 1.42 + 0.04 + 0.04 + 0.04 + 0.04 + 0.04 + 0.04 Simplify: S < 1.42 + 0.24 Simplify: S < 1.66 GMAT club
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2020-01-01 18:25:55
236744s
该数列可以用正方形来解，相当于10个正方形的面积，总面积小于1.5
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2019-10-26 16:48:58
206030zwiis
1+1/4+1/9………<1+1/（1*2）+1/（2*3）……=1-1/10=9/10<2
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2019-09-28 21:22:07
Aliceee
S = 1 + 1/2²+ 1/3²+ 1/4²+ 1/5²+ 1/6²+ 1/5²+ 1/8²+ 1/9²+ 1/10² = 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/64 + 1/72 1/4=0.25，1/9≈0.11<0.1，1/25=0.04,1/64和1/72就基本上可以忽略不计了。 = 1 + 0.25 + 0.11 + 0.04 ≈ 1.4 正确答案: E
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2018-09-05 02:00:43
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