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a,Đặt \(A=\frac{1}{1\times4}+\frac{1}{4\times7}+...+\frac{1}{97\times100}\)
\(\Rightarrow3A=\frac{3}{1\times4}+\frac{3}{4\times7}+...+\frac{3}{97\times100}\)
\(\Rightarrow3A=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\)
\(\Rightarrow3A=1-\frac{1}{100}=\frac{99}{100}\)
\(\Rightarrow A=\frac{99}{300}\)
b, \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{99}{100}=\frac{1\times2\times...\times99}{2\times3\times...\times1000}=\frac{1}{100}\)
c, \(\frac{3}{4}\times\frac{8}{9}\times...\times\frac{99}{100}=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times...\times\frac{9.11}{10.10}=\frac{1.2.....9}{2.3.....10}\times\frac{3.4.....11}{2.3.....10}=\frac{1}{10}\times\frac{11}{2}=\frac{11}{20}\) (dấu . là dấu nhân)
a)\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}......\frac{99}{100}\)
\(=\frac{1.2.3.4.....99}{2.3.4.5.6.....100}\)
\(=\frac{1}{100}\)
b) Tương tự như câu a
1 gấp 10 lần 1/10
1/10 : 1/100 = 10
1/100 : 1/1000 = 10
1 : 1/10 = 10
1/10 gấp 10 lần 1/100
1/100 gấp 10 lần 1/1000
k mình nha
Mình không chắc đã đúng đâu nhưng mình cứ giair thử nhé !
Ta có :
A = \(\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\)+ ... + \(\frac{1}{99}-\frac{1}{100}\)
= \(\left(\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+...\frac{1}{99}\right)\)- \(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}...+\frac{1}{100}\right)\)
= \(\left(\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+...\frac{1}{99}\right)\)+ \(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}...+\frac{1}{100}\right)\)
- \(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{100}\right)\)x 2
= \(\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\)- \(\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)\)
= \(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{100}\)= B
Vậy , A = B
~ Chúc bạn học giỏi ! ~
\(=\frac{6}{5}\times\frac{7}{6}\times...\times\frac{11}{10}\)(lại lỗi đề)
\(=\frac{6×7×...×11}{5×6×...×10}\)
\(=\frac{11}{5}\)
\(1\frac{1}{5}\cdot1\frac{1}{6}\cdot1\frac{1}{7}\cdot1\frac{1}{8}\cdot1\frac{1}{9}\cdot1\frac{1}{10}\)
\(=\frac{6}{5}\cdot\frac{7}{6}\cdot\frac{8}{7}\cdot\frac{9}{8}\cdot\frac{10}{9}\cdot\frac{11}{10}\)
\(=\frac{6\cdot7\cdot8\cdot9\cdot10\cdot11}{5\cdot6\cdot7\cdot8\cdot9\cdot10}\)
\(=\frac{11}{5}\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{99}{100}\)
\(=\frac{1}{100}\)
♥ ☼ ↕ ✿ ⊰ ⊱ ✪ ✣ ✤ ✥ ✦ ✧ ✩ ✫ ✬ ✭ ✯ ✰ ✱ ✲ ✳ ❃ ❂ ❁ ❀ ✿ ✶ ✴ ❄ ❉ ❋ ❖ ⊹⊱✿ ✿⊰⊹ ♧ ✿
\(=\frac{1}{2\cdot3:2}+\frac{1}{3\cdot4:2}+\frac{1}{4\cdot5:2}+...+\frac{1}{50\cdot51:2}\)
\(=\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+...+\frac{2}{100\cdot101}\)
\(=2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{50\cdot51}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{50}-\frac{1}{51}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{51}\right)=\frac{1}{2}\cdot\frac{49}{102}=\frac{49}{204}\)
=36
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