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\(\frac{2.6.10+6.10.14+10.14.18+...+194.198.202}{1.3.5+3.5.7+...+97.99.101}\)
\(=\frac{2^3.1.3.5+2^3.3.5.7+2^3.97.99.101}{1.3.5+3.5.7+...+97.99.101}\)
\(=\frac{2^3\left(1.3.5+3.5.7+...+97.99.101\right)}{1.3.5+3.5.7+...+97.99.101}\)
\(=\frac{2^3}{1}=8\)
Vậy A = 8
a) A = 1/3 - 1/7 + 1/7 - 1/11 +......+1/107 - 1/111
A = 1/3 - 1/111
A = ..............Bạn tự tính nhé!
b) B = 2.(3/15.18 + 3/18.21 +........+3/87.90)
B = 2.(1/15 - 1/18 + 1/18 - 1/21 +........+1/87 - 1/90)
B = 2.(1/15 - 1/90)
B = 2.5/90
B =......Tự tính nhé!
C ; D làm tương tự nhé!
a, A= \(5\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\right)\)
\(A=5\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(A=5\left(1-\dfrac{1}{100}\right)\)
\(A=5.\dfrac{99}{100}=\dfrac{99}{20}.\)
b, \(C=1.2.3+2.3.4+...+8.9.10\)
\(4C=1.2.3.4+2.3.4.\left(5-1\right)+...+8.9.10.\left(11-7\right)\)\(4C=1.2.3.4+2.3.4.5-1.2.3.4+...+8.9.10.11-7.8.9.10\)\(4C=8.9.10.11\)
\(C=\dfrac{8.9.10.11}{4}=1980.\)
c, https://hoc24.vn/hoi-dap/question/384591.html
Câu này bạn vào đây mình đã giải câu tương tự nhé.
\(1)A=\dfrac{5}{1.2}+\dfrac{5}{2.3}+...+\dfrac{5}{99.100}\)
\(\Leftrightarrow A=5\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(\Leftrightarrow A=5\left(1-\dfrac{1}{100}\right)\)
\(\Leftrightarrow A=5\cdot\dfrac{99}{100}\)
\(\Leftrightarrow A=\dfrac{99}{20}\)
\(\frac{2.2}{1.3}x\frac{3.3}{2.4}x\frac{4.4}{3.5}x\frac{5.5}{4.6}x\frac{6.6}{5.7}\)=\(2.\frac{2}{3}.\frac{3}{2}.\frac{3}{4}.\frac{4}{3}.\frac{4}{5}.\frac{5}{4}.\frac{5}{6}.\frac{6}{5}.\frac{6}{7}\)
\(=2.\frac{6}{7}=\frac{12}{7}\)
22/1.3 × 32/2.4 × 42/3.5 × 52/4.6 × 62/5.7
= 2.3.4.5.6/1.2.3.4.5 × 2.3.4.5.6/3.4.5.6.7
= 6 × 2/7
= 12/7
d)\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}=\frac{2.3+2.2.6+2.7.21}{3.5+3.2.10+3.7.35}=\frac{2.3+2.12+2.147}{3.5+3.20+3.245}=\frac{2\left(3+12+147\right)}{3\left(5+20+245\right)}\)
\(=\frac{2.162}{3.270}=\frac{54}{135}=\frac{2}{5}\)
\(a.\frac{-2019.2018+1}{\left(-2017\right).\left(-2019\right)+2018}\)
\(=\frac{2019.\left(-2018\right)+1}{2019.2017+2018}\)
\(=\frac{2019.\left(-2018\right)+1}{2019.2018-1}\)
\(=-\frac{2018}{2018}\)
\(=-1\)
ta có: \(\frac{2^5.7+2^5}{2^5.2^5-2^5.3}=\frac{2^5.\left(7+1\right)}{2^5.\left(2^5-3\right)}=\frac{8}{2^5-3}=\frac{8}{29}=\frac{104}{377}\)
\(\frac{3^4.5.\left(-3\right)^6}{3^4.13.3^4}=\frac{3^{10}.5}{3^8.13}=\frac{3^2.5}{13}=\frac{45}{13}=\frac{1305}{377}\)
\(\Rightarrow\frac{104}{377}< \frac{1305}{377}\Rightarrow\frac{2^5.7+2^5}{2^5.2^5-2^5.3}< \frac{3^4.5.\left(-3\right)^6}{3^4.13.3^4}\)
Ta cứ tính ra tử số và mỗi số của từng phân số ra nhé Jerry Gaming:
\(\frac{2^5.7+2^5}{2^5.2^5-2^5.3}\)= \(\frac{2^5.\left(7+1\right)}{2^5.\left(2^5-3\right)}=\frac{2^5.8}{2^5.\left(32-3\right)}=\frac{32.8}{2^5.29}=\frac{32.8}{32.29}=\frac{8}{29}\)
\(\frac{3^4.5.\left(-3\right)^6}{3^4.13.3^4}\)= \(\frac{3^4.5.3^6}{3^8.13}=\frac{3^{10}.5}{3^8.13}=\frac{3^2.5}{13}=\frac{9.5}{13}=\frac{45}{13}\)
\(\frac{8}{29}\)và \(\frac{45}{13}\)MSC: 377
Ta có:
\(\frac{8}{29}=\frac{8.13}{29.13}=\frac{104}{377}\)
\(\frac{45}{13}=\frac{45.29}{13.29}=\frac{1305}{377}\)
Vậy quy đồng \(\frac{2^5.7+2^5}{2^5.2^5-2^5.3}\)và \(\frac{3^4.5.\left(-3\right)^6}{3^4.13.3^4}\)ta được \(\frac{104}{377}\)và \(\frac{1305}{377}\)
Chúc bạn học tốt!
\(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}\)
\(A=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(A=2.\left(1-\frac{1}{7}\right)\)
\(A=2.\frac{6}{7}\)
\(A=\frac{12}{7}\)
\(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}\)
\(A=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(A=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\right)\)
\(A=2.\left(1-\frac{1}{7}\right)\)
\(A=2.\left(\frac{7}{7}-\frac{1}{7}\right)\)
\(A=2.\frac{6}{7}\)
\(A=\frac{12}{7}\)
Chúc bạn học tốt !!!