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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.
\(1)A=\dfrac{5}{1.2}+\dfrac{5}{2.3}+...+\dfrac{5}{99.100}\)
\(\Leftrightarrow A=5\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(\Leftrightarrow A=5\left(1-\dfrac{1}{100}\right)\)
\(\Leftrightarrow A=5\cdot\dfrac{99}{100}\)
\(\Leftrightarrow A=\dfrac{99}{20}\)
\(\frac{\left(-2\right)^3.3^3.5^3.7.8}{3.5^3.2^4.42}\)
\(=\frac{\left(-2\right)^3.3^3.5^3.7.2^3}{3.5^3.2^4.2.3.7}=\frac{\left(-2\right)^3.3^3.5^3.7.2^3}{3^2.5^3.2^5.7}=\frac{-2.3}{1}=-6\)
học tốt~~~
\(B=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+\dfrac{2}{4.5.6}+\dfrac{2}{5.6.7}+\dfrac{2}{6.7.8}\)
\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{6.7}-\dfrac{1}{7.8}\)
\(=\dfrac{1}{1.2}-\dfrac{1}{7.8}\)
\(=\dfrac{1}{2}-\dfrac{1}{56}=\dfrac{27}{56}\)
\(=\frac{2^3.3^3.5^3.2^3.7}{3.2^4.5^3.2.7}=\frac{2^6.5^3.3^3}{3.2^5.5^3}=2.3^2=2.9=18\)
\(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2.2^9}\)
=\(\frac{\left(\frac{2}{5}.5\right)^7+\left(\frac{9}{4}:\frac{3}{16}\right)^3}{2^7.5^2.2^9}\)
=\(\frac{2^7+\left(\frac{9}{4}.\frac{16}{3}\right)^3}{2^7.5^2.2^9}\)
=\(\frac{2^7+3^3.4^3}{2^7.5^2.2^9}\)
=\(\frac{2^7+3^3.2^6}{2^7.5^2.2^9}\)
=\(\frac{2^6.\left(27+2\right)}{2^6.5^2.2^{10}}\)
=\(\frac{29}{25600}\)
Đoạn \(\frac{2^6\cdot\left(27+2\right)}{2^6\cdot5^2\cdot2^{10}}\)là sai rồi bn ơi!!!
Bn phải lm như mục trên là:
\(\frac{2^6\left(2+3^3\right)}{2^7\left(5^2+2^2\right)}\)\(=\frac{2^6\cdot29}{2^7\cdot29}=\frac{1}{2}\)
Nhưng dù sao cx c.ơn bn vì đã giúp mk,mk sẽ cho bn 1 ths nka!!!
\(=\frac{\left(2^2\right)^5.2.5.5^6+2^8.\left(5^2\right)^5}{2^8.5^4+2^5.5^7}=\frac{2^{10}.2.5^7+2^8.5^{10}}{2^5.5^4\left(2^3+5^3\right)}=\frac{2^{11}.5^7+2^8.5^{10}}{2^5.5^4.\left(2^3+5^3\right)}=\frac{2^8.5^7\left(2^3+5^3\right)}{2^5.5^4\left(2^3+5^3\right)}=\frac{2^3.5^3.1}{1.1.1}=1000\)
\(A=\frac{3^5\cdot1^7+3^9\cdot5}{3^7\cdot2^5}=\frac{3^5\left(1+405\right)}{3^7\cdot32}=\frac{406}{288}=\frac{203}{144}\)
A= \(\frac{3^5.1^7+3^9.5}{3^7.2^5}\)= \(\frac{3^5+3^5.3^4.5}{3^7.2^5}\)= \(\frac{3^5\left(1+81.5\right)}{3^7.2^5}\)= \(\frac{3^5\left(1+405\right)}{3^7.2^5}\)= \(\frac{406}{3^2.2^5}\)= \(\frac{406}{9.32}\)= \(\frac{203}{9.16}\)= \(\frac{203}{144}\).
Vậy A= \(\frac{203}{144}\).
A=(2.23.25.27.211)(52.54.58.516)
A=21+3+5+7+11.52+4+8+16
A=227.530
A=227.527.53
A=(227.527).125
A=(2.5)27.125
A=1027.125
Vậy A có 27 chữ số 0 tận cùng