CHO: S= 3/1x4 + 3/4x7 + 3/7x10 +......+ 3/n(n+3)
CHỨNG MINH RẰNG S bé hơn 1
cho M= 1/31+1/32+1/33+...+1/60
Chứng minh rằng3/5<M<4/5
Cho S=3/1x4+3/4x7+3/7x10+...+3/n(n+3)
Chứng minh rằng S<1
cho S = 3/1x4 + 3/4x7 + 3/7x10+ ...+3/40x43 + 3/43x46.Hãy chứng minh S<1
= 1/1-1/4+1/4-1/7+1/7-1/10+...+1/40-1/43+1/43-1/46
= 1 - 1/46 = 45/46 < 1
Cho: S=\(\frac{3}{1x4}+\frac{3}{4x7}+\frac{3}{7x10}+...+\frac{3}{100x103}\). Chứng minh S<1
S=1/1-1/4+1/4+1/7-1/7+1/10+...+1/100-1/103
S=1/1-1/103
S=102/103
Vì 102/103<1 nên S<1
\(S=\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+...+\frac{3}{100\cdot103}\)
\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{100}-\frac{1}{103}\)
\(S=1-\frac{1}{103}\)
\(S=\frac{102}{103}< 1\)
\(\frac{3}{1x4}+\frac{3}{4x7}+\frac{3}{7x10}+.......+\frac{3}{100x103}\)
\(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}....+\frac{1}{100}-\frac{1}{103}\)
\(=\frac{1}{1}-\frac{1}{103}\)
=\(\frac{102}{103}\)
Cho S=3/1x4+3/4x7+3/7x10+...+3/40x43+3/43x46. Hãy chứng tỏ S<1
Cho S=3/1x4+3/4x7+3/7x10+...+3/40x43+3/43x46. Hãy chứng tỏ S<1
ĐPM : S < 1
S=3/1x4+3/4x7+3/7x10+...+3/40x43+3/43x46
\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{46}\)
\(S=1-\frac{1}{46}\)
=>S<1
S = 3/1.4 + 3/4.7 +....+ 3/43.46
S = 1 - 1/4 + 1/4 - 1/7 +.....+ 1/43 - 1/46
S = 1 - 1/46
S = 45/46 < 1
=> S < 1 (đpcm)
Tính tổng : S= 3/1x4 + 3/4x7 + 3/7x10 + ........... + 3/37x40
=1-1/4+1/4-1/7+1/7-...+1/37-1/40
=1-1/40=39/40
chứng tỏ tổng sau nhỏ hơn 1:A=3/1x4+3/4x7+3/7x10+.....+3/40x43
\(A=\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+.....+\dfrac{3}{40.43}\)
\(A=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+.....+\dfrac{1}{40}-\dfrac{1}{43}\)
\(A=1-\dfrac{1}{43}\)
\(A< 1\left(đpcm\right)\)
\(A=3\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{40}-\dfrac{1}{43}\right)\)
\(=3\left(1-\dfrac{1}{43}\right)=\dfrac{126}{43}>1\)
... sai đâu không nhỉ??
3/1x4+3/4x7+3/7x10+...+3/nx(n+3)
A=\(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{2.\left(x+3\right)}\)
=> A=\(\frac{3}{1}-\frac{3}{4}+\frac{3}{4}+...+\frac{3}{2.x}-\frac{3}{2.\left(x+3\right)}\)
=> A =\(\frac{3}{1}-\frac{3}{2.\left(x+3\right)}\)
s = cho 3/1x4 + 3/4x7+....+3/43x46 chứng tỏ s>1
\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{46}\)
\(S=1-\frac{1}{46}<1\)
=>chứng minh bị sai hoặc đề sai
S=\(\frac{3}{1.4}+\frac{3}{4.7}+...........+\frac{3}{43.46}\)
=\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...........+\frac{1}{43}-\frac{1}{46}\)
=\(1-\frac{1}{46}<1\)
\(\Rightarrow S<1\)
S = 3/1.4 + 3/4.7 + ... + 3/43.46
= 3 - 3/4 + 3/4 - 3/7 + ... + 3/43 - 3/46
= 135/46 > 1.
=> S > 1.
=> Điều cần chứng minh.
3 Tính nhanh
3/1x4+3/4x7+3/7x10+3/10x13+3/13x16=?
=1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16
=1-1/16=15/16