Câu 5.(0,5 đ)

b, Chứng tỏ rằng  A =1+3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷ + 3⁸+ 3⁹ + 3¹⁰ + 3¹¹ chia hết cho 40.

Có: \(\frac{1}{2^{2}} < \frac{1}{1.2} ; \frac{1}{3^{2}} < \frac{1}{2.3} ; . . . ; \frac{1}{8^{2}} < \frac{1}{7.8}\)

\(\Rightarrow B < \frac{1}{1.2} + \frac{1}{2.3} + . . . + \frac{1}{7.8}\)

\(\Rightarrow B < 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + . . . + \frac{1}{7} - \frac{1}{8}\)

\(\Rightarrow B < 1 - \frac{1}{8} < 1\)

\(\Rightarrow B < 1\) \(\Rightarrow đ p c m\)

Có: \(\frac{1}{2^{2}} < \frac{1}{1.2} ; \frac{1}{3^{2}} < \frac{1}{2.3} ; . . . ; \frac{1}{8^{2}} < \frac{1}{7.8}\)

\(\Rightarrow B < \frac{1}{1.2} + \frac{1}{2.3} + . . . + \frac{1}{7.8}\)

\(\Rightarrow B < 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + . . . + \frac{1}{7} - \frac{1}{8}\)

\(\Rightarrow B < 1 - \frac{1}{8} < 1\)

\(\Rightarrow B < 1\) \(\Rightarrow đ p c m\)

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