Question

13数学题详解

Answer 1

选A，分析如下：
输入n=10时，此时i=2 符合　i≤n,程序进入循环，运算S，结果为：
S=0+1/(i²－1）
=0+1/(2²-1)
=1/3
i=i+2 结果i=4　符合　i≤n,程序进入循环，运算S
S=1/3+1/(4²-1)
=2/5
i=1+2 结果i=6 符合　i≤n,程序进入循环，运算S
S=2/5+1/(6²-1)
=3/7
i=1+2 结果i=8 符合　i≤n,程序进入循环，运算S
S=3/7+1/(8²-1)
=4/9
i=1+2 结果i=10 符合　i≤n,程序进入循环，运算S
S=4/9+1/(8²-1)
=5/11
i=1+2 结果i=12 不符合 i≤n 　程序跳出循环，输出S
故可得S＝5/11 选A

Answer 2

S=1/(4-1)+1/(16-1)+1/(36-1)+1/(64-1)+1/(100-1)
=1/3+1/15+1/35+1/63+1/99
=1/3+（1/2）(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/3+(1/2)×(8/33)
=1/3+4/33
=15/33;
=5/11;
选A

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Answer 3

1/3+1/15+1`/35+1/63+1/99
=6/15+1/35+1/63+1/99
=2/5+1/35+1/63+1/99
=15/35+1/63+1/99
=3/7+1/63+1/99
=28/63+1/99
=(28*11+7)/63*11
=315/63*7
=105/21*11
=35/77
=5/11
(A)
1/n^2-1

Answer 4

输出的S=1/3+1/15+1/35+1/63+1/99
=1/3+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)
=1/3+1/6-1/22
=1/2-1/22
=5/11
选A

Answer 5

S=1/(4-1)+1/(16-1)+1/(36-1)+1/(64-1)+1/(100-1)
=1/3+1/15+1/35+1/63+1/99
=1/3+（1/2）(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/3+(1/2)×(8/33)
=1/3+4/33
=15/33;
=5/11;
选A