Question

[đặng vũ hải lâm]

so sánh các phân sos sau ko quy dồng mẫu số

13/15 và 45/47

35/65 và 17/47

2 tính nhanh

2/3 + 2/15 + 2/35 + 2/63 +............+2/101x103

4/1/5 + 4/5x9 +...............+ 4/101 x105

Answer 1

[Mạc Quân]

\(\frac{13}{15}=1-\frac{2}{15};\frac{45}{47}=1-\frac{2}{47}\)

\(\text{mà }\frac{2}{15}>\frac{2}{47}\Rightarrow\frac{13}{15}< \frac{45}{47}\)
\(\frac{35}{65}=1-\frac{30}{65};\frac{17}{47}=1-\frac{30}{47}\)
\(\text{mà }\frac{30}{65}< \frac{30}{47}\Rightarrow\frac{35}{15}>\frac{17}{47}\)

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{101.103}\)
\(\Rightarrow\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{101}-\frac{2}{103}\)
\(\Rightarrow2-\frac{2}{103}=\frac{204}{103}\)
\(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{101.105}\)
\(\Rightarrow4-\frac{4}{5}+\frac{4}{5}-\frac{4}{9}+...+\frac{4}{101}-\frac{4}{105}\)
\(\Rightarrow4-\frac{4}{105}=\frac{416}{105}\)