Question

Cho S = \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7\cdot10}+....+\frac{3}{40\cdot43}+\frac{3}{43\cdot46}\)   . Hay chung to rang S < 1

Answer 1

\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{46}\)

\(s=1-\frac{1}{46}< 1\)

Vậy S<1

Answer 2

\(S=\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+...+\frac{3}{43\cdot46}\)

\(S=1\left[\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+...+\frac{1}{43\cdot46}\right]\)

\(S=1\left[1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{46}\right]\)

\(S=1\left[1-\frac{1}{46}\right]=1\cdot\frac{45}{46}=\frac{45}{46}< 1(đpcm)\)

Answer 3

 S = \(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{40}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}\)

S = \(\frac{1}{1}-\frac{1}{46}\)

S = \(\frac{46}{46}-\frac{1}{46}\)

S = \(\frac{45}{46}< 1\)

Hay S < 1

Vậy S < 1 (đpcm)

Answer 4

\(S=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{40.43}+\frac{3}{43.46}\)

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{40}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}\)

\(=1-\frac{1}{46}\)

\(=\frac{46}{46}-\frac{1}{46}=\frac{45}{46}\)

\(\Rightarrow S=\frac{45}{46}\)

\(\Rightarrow S< 1\left(đpcm\right)\)

Answer 5

\(A=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{40.43}+\frac{3}{43.46}\)

  \(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{40}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}\)

  \(=1-\frac{1}{46}\)

  \(=\frac{45}{46}\)

=> S < 1     

Study well ! >_<