1. Cho S = 3/1.4 + 3/4.7 + 3/7.10 + … + 3/40.43 + 3/43.46 . Chứng tỏ S < 1 16/10/2021 Bởi Remi 1. Cho S = 3/1.4 + 3/4.7 + 3/7.10 + … + 3/40.43 + 3/43.46 . Chứng tỏ S < 1
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- $\frac{1}{46}$ = $\frac{45}{46}$ <1 ⇒ S <1 Bình luận
Đáp án: S=3/1.4+3/4.7+3/7.10+ … +3/40.43+3/43.46 = 1/1.4+1/4.7+1/7.10+ … +1/40.43+1/43.46 = 1/1-1/4+1/4-1/7+1/7-1/10+…+1/40-1/43+1/43-1/46 = 1/1-1/46 = 45/46 < 1 => S < 1 Bình luận
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- $\frac{1}{46}$
= $\frac{45}{46}$ <1
⇒ S <1
Đáp án:
S=3/1.4+3/4.7+3/7.10+ … +3/40.43+3/43.46
= 1/1.4+1/4.7+1/7.10+ … +1/40.43+1/43.46
= 1/1-1/4+1/4-1/7+1/7-1/10+…+1/40-1/43+1/43-1/46
= 1/1-1/46
= 45/46 < 1
=> S < 1