Câu hỏi của Phan Lê Thảo Nguyên

Question

So Sánh: E=3/21+3/22+3/23+3/24+3/25+...+3/29+3/30 với M=3/2

Kevin · Accepted Answer

Vì: $\frac{3}{21}=\frac{3}{21}$$\frac{3}{22}$ < $\frac{3}{21}$$\frac{3}{23}$ < $\frac{3}{21}$$\frac{3}{24}$<$\frac{3}{21}$$\frac{3}{25}$< $\frac{3}{21}$.....$\frac{2}{29}$<$\frac{3}{21}$$\frac{2}{30}$<$\frac{3}{21}$Nên $\frac{3}{21}+\frac{3}{22}+\frac{3}{23}+\frac{3}{24}+\frac{3}{25}+...+\frac{3}{29}+\frac{3}{30}$ < $\frac{3}{21}.10$Ta có: $\frac{3}{21}.10$ = $\frac{10}{7}$Mà $\frac{10}{7}$ < $\frac{3}{2}$=>$\frac{3}{21}+\frac{3}{22}+\frac{3}{23}+\frac{3}{24}+\frac{3}{25}+...+\frac{3}{29}+\frac{3}{30}$ < $\frac{3}{2}$Vậy E < MCâu trả lời: Vì: $\frac{3}{21}=\frac{3}{21}$$\frac{3}{22}$ < $\frac{3}{21}$$\frac{3}{23}$ < $\frac{3}{21}$$\frac{3}{24}$<$\frac{3}{21}$$\frac{3}{25}$< $\frac{3}{21}$.....$\frac{2}{29}$<$\frac{3}{21}$$\frac{2}{30}$<$\frac{3}{21}$Nên $\frac{3}{21}+\frac{3}{22}+\frac{3}{23}+\frac{3}{24}+\frac{3}{25}+...+\frac{3}{29}+\frac{3}{30}$ < $\frac{3}{21}.10$Ta có: $\frac{3}{21}.10$ = $\frac{10}{7}$Mà $\frac{10}{7}$ < $\frac{3}{2}$=>$\frac{3}{21}+\frac{3}{22}+\frac{3}{23}+\frac{3}{24}+\frac{3}{25}+...+\frac{3}{29}+\frac{3}{30}$ < $\frac{3}{2}$Vậy E < M

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