Question

Cho S=\(\frac{3}{1.4}\)+\(\frac{3}{4.7}\)+\(\frac{3}{7.10}\)+....\(\frac{3}{40.43}\)+\(\frac{3}{43.46}\). Hãy chứng tỏ rằng S<1.

Answer 1

           Bài làm :

Ta có :

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

\(S=\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+...+\frac{43-40}{40.43}+\frac{46-43}{43.46}\)

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

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

=> Điều phải chứng minh

Answer 2

S=1-1/4+1/4-1/7+1/7-1/10+...+1/40-1/43+1/43-1/46

S=1-1/46 S=45/46<1 

vậy S <1 

 

Answer 3

ta có:3/1.4+3/4.7+....=3/43.46 suy ra 1(1/1-1/4+...+1/43-1/46) suy ra 1(1/1-1/46)= 1.45/46=45/46                                                                         do 45/46<1 suy ra 3/1.4+3/4.7+...+3/43.46<1(DPCM)

Answer 4

S= 1/1 - 1/4 +1/4- 1/7+1/7-1/10+......+ 1/40- 1/43 +1/43-1/46

S=1/1-1/46

S=45/46

Vì 45/46 <1 nên S<1

Answer 5

s = 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ..........+ 1/40 - 1/43 - 1/46

s = 1- 1/46

s = 45/46 < 1

vậy s < 1