toan kho day

K

khanhchi_cut3

tinh

S = 1 - 1/2² - 1/3² - 1/4² -.. - 1/10²
- - -
Có: 1/k² < 1/(k-1)k = 1/(k-1) - 1/k (với mọi k nguyên, k > 1)

1/2² < 1 /1.2 = 1/1 - 1/2
1/3² < 1 /2.3 = 1/2 - 1/3
...
1/10² < 1 /9.10 = 1/9 - 1/10
+ + + cộng vế lại + + +
1/2² + 1/3² +..+ 1/10² < 1 - 1/10

=> -1/2² - 1/3² - .. - 1/10² > -1 + 1/10

=> 1 - 1/2² - 1/3² - .. - 1/10² > 1/10 > 0 (đpcm)
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:)>-
 
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