Bài toán đại tốt nghiệp vào 10 không chuyên

L

le_tien

[TEX]n^2 + (n+1)^2 = 2n^2 + 2n + 1 > 2n(n+1)[/TEX]
[TEX]\Rightarrow \frac{1}{n^2 + (n+1)^2} < \frac{1}{2n(n+1)} = \frac{1}{2} . ( \frac{1}{n} - \frac{1}{n+1})[/TEX]
[TEX]\Rightarrow S < \frac{1}{2}. (1 - \frac{1}{2009}) < \frac{1}{2} [/TEX]
 
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