Question

so sánh A với 1 , biếtA = \(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)

Answer 1

A=...

<=>\(A=\frac{1}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{1}{17.20}\right)\)

<=>\(A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right)\)

<=>\(A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{20}\right)\)

<=>\(A=\frac{1}{6}-\frac{1}{60}< \frac{1}{6}< 1\)

Answer 2

sai ùi 

Answer 3

\(A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right)\)

\(A=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(A=\frac{1}{3}.\frac{9}{20}\)

\(A=\frac{3}{20}\)

Vì \(\frac{3}{20}< 1\Rightarrow A< 1\)

Answer 4

A=1/2.5+1/5.8+1/8.11+1/11.14+1/14.17+1/17.20

A=2/2.(1/2.5+1/5.8+1/8.11+1/11.14+1/14.17+1/17.20)

A=1/2.(2/2.5+2/5.8+2/8.11+2/11.14+2/14.17+2/17.20)

A=1/2.(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20)

A=1/2.(1/2-1/20)

A=1/2.9/20

A=9/40

Vì 9/40 <1 nên A<1

Answer 5

A=1/2.5+1/5.8+1/8.11+1/11.14+1/14.17+1/17.20

=>A.3=3/2.5+3/5.8+3/8.11+3/11.14+3/14.17+3/17.20

=>A.3=1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20

=>A.3=1/2-1/20=9/20

=>A=9/20:3

=>A=3/20

Vì 3/20<1 mà 3/20 =A

=>A<1

Vậy A<1 

Answer 6

\(A=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\)\(\frac{1}{14.17}+\frac{1}{17.20}\)

\(A=\)\(\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\right)\)

\(A=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(A=\frac{1}{3}.\frac{9}{20}\)

\(A=\frac{3}{20}\)

\(Vì\)\(\frac{3}{20}< 1\)

\(\Rightarrow A< 1\)