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= \(\frac{1}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-.....+\frac{1}{x}-\frac{1}{x+1}\right)\) )
= \(\frac{1}{3}\left(1-\frac{1}{x+1}\right)\)
=\(\frac{1}{3}x\left(\frac{x+1}{x+1}-\frac{1}{x+1}\right)\)
= \(\frac{1}{3}x\frac{x}{x+1}\)
Bài 1:
$M=3.4.5+4.5.6+...+13.14.15$
$4M=3.4.5(6-2)+4.5.6(7-3)+....+13.14.15(16-12)$
$=-2.3.4.5+3.4.5.6-3.4.5.6+4.5.6.7+....-12.13.14.15+13.14.15.16$
$=-2.3.4.5+13.14.15.16=43560$
$M=43560:4=10890$
Bài 2:
a.
$3M=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}$
$=\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+...+\frac{100-97}{97.100}$
$=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}$
$=1-\frac{1}{100}=\frac{99}{100}$
$M=\frac{99}{100}:3=\frac{33}{100}$
\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{46}\)
\(S=1-\frac{1}{46}<1\)
=>chứng minh bị sai hoặc đề sai
S=\(\frac{3}{1.4}+\frac{3}{4.7}+...........+\frac{3}{43.46}\)
=\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...........+\frac{1}{43}-\frac{1}{46}\)
=\(1-\frac{1}{46}<1\)
\(\Rightarrow S<1\)
\(C=\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{52.55}+\frac{1}{55.58}\)
\(\Rightarrow C=\frac{1}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{52.55}+\frac{3}{55.58}\right)\)
\(\Rightarrow C=\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{52}-\frac{1}{55}+\frac{1}{55}-\frac{1}{58}\right)\)
\(\Rightarrow C=\frac{1}{3}.\left(1-\frac{1}{58}\right)\)
\(\Rightarrow C=\frac{1}{3}.\frac{57}{58}\)
\(\Rightarrow C=\frac{19}{58}\)
Vậy \(C=\frac{19}{58}\)
~ Ủng hộ nhé
\(3C=\frac{3}{1\times4}+\frac{3}{4\times7}+...+\frac{1}{55\times58}..\)
\(3C=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}....+\frac{1}{55}-\frac{1}{58}..\)
\(3C=1-\frac{1}{58}=\frac{57}{58}\)
\(C=\frac{57}{174}\)
\(S=\frac{1}{1\times4}+\frac{1}{4\times7}+\frac{1}{7\times10}+...+\frac{1}{94\times97}+\frac{1}{97\times100}\)
\(S=\frac{1}{3}\times\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}+\frac{1}{97}-\frac{1}{100}\right)\)
\(S=\frac{1}{3}\times\left(\frac{1}{1}-\frac{1}{100}\right)\)
\(S=\frac{1}{3}\times\frac{99}{100}\)
\(S=\frac{33}{100}\)
1/1.4+1/4.7+1/7.10+1/10.13+1/13.16
=1/3.(3/1.4+3/4.7+3/7.10+3/10.13+3/13.16)
=1/3.(1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3.(1/1-1/16)
=1/3.(16/16-1/16)=1/3.15/16=5/16
mà mình không phải là Thiên Tỷ mình tên là Gia Yến đấy nhé