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1. A - B = 40+ 3/8 + 7/8² + 5/8³ + 32/8^{5 -} (24/8² + 40+ 5/8² + 40/8⁴ + 5/8^{4 )}

⁼ 40.8⁵/8⁵ + 3.8⁴/8⁵ + 7.8³/8⁵ + 5.8²/8⁵ + 32/8⁵ - 24.8³/8⁵ - 40.8⁵/8⁵ - 5.8³/8⁵ - 40.8/8⁵ - 5.8/8⁵

⁼ 40.8⁵/8⁵ + 24.8³/8⁵ + 7.8³/8⁵ + 5.8²/8⁵ + 32/8⁵ - 24.8³/8⁵ - 40.8⁵/8⁵ - 5.8³/8⁵ - 40.8/8⁵ - 5.8/8⁵

⁼ 7.8³/8⁵ + 5.8²/8⁵ + 32/8⁵ - 5.8³/8⁵ - 40.8/8⁵ - 5.8/8⁵

⁼ 7.8³/8⁵ + 5.8²/8⁵ -8/8⁵ - 5.8³/8⁵ - 40.8/8⁵

= 2.8³/8⁵ + 5.8²/8⁵ - 40.8/8⁵ - 8/8⁵

= 2.8³/8⁵ + 40.8/8⁵ - 40.8/8⁵ - 8/8⁵

= 2.8³/8⁵  - 8/8⁵ > 0 

Vay A > B

ai so sanh C va D di ma duoc thi minh se tink cho

Rút gọn từng phân số rồi sắp xếp lại như sau :

\(A=\left(40+\frac{3}{8}+\frac{5}{8^3}\right)+\left(\frac{7}{8^2}+\frac{4}{8^4}\right)\)

\(B=\left(40+\frac{3}{8}+\frac{5}{8^3}\right)+\left(\frac{5}{8^2}+\frac{5}{8^4}\right)\)

Rõ ràng để so sánh A với B chỉ cần so sánh \(\frac{7}{8^2}+\frac{4}{8^4}\) với \(\frac{5}{8^2}+\frac{5}{8^4}\) .

Ta có :

\(\frac{7}{8^2}+\frac{4}{8^4}=\left(\frac{5}{8^2}+\frac{4}{8^4}\right)+\frac{2}{8^2}\)

còn \(\frac{5}{8^2}+\frac{5}{8^4}=\left(\frac{5}{8^2}+\frac{4}{8^4}\right)+\frac{1}{8^4}\)

Do \(\frac{2}{8^2}>\frac{1}{8^4}\) nên \(\frac{7}{8^2}+\frac{4}{8^4}>\frac{5}{8^2}+\frac{5}{8^4}\) . Từ đó suy ra A > B.