Question

[Cô Bé Yêu Đời]

a) \(E=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{48.49.50}\)

b) \(F=\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

c) \(G=\frac{636363.37-373737.63}{1+2+3+...+2017}\)

d) \(H=\left(\frac{12+\frac{12}{19}-\frac{12}{37}-\frac{12}{53}}{3+\frac{1}{3}-\frac{3}{37}-\frac{3}{53}}:\frac{4+\frac{4}{17}+\frac{4}{19}+\frac{4}{2016}}{5+\frac{5}{17}+\frac{5}{19}+\frac{5}{3016}}\right).\frac{124242423}{237373735}\)

giúp mk với ! Help me!

Answer 1

[*♥•♦♫••♥* Yuzakuchi *♥•♦♫••♥*]

c) G = \(\frac{636363.37-373737.63}{1+2+3+...+2017}\)

G = \(\frac{63.10101.37-37.10101.63}{1+2+3+...+2017}\)

G = \(\frac{0}{1+2+3+...+2017}\)

=> G = 0

Vậy G = 0

Answer 2

[Nguyễn Huy Tú]

a) \(E=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{48.49.50}\)

\(\Rightarrow E=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{48.49.50}\right)\)

\(\Rightarrow E=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)

\(\Rightarrow E=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{49.50}\right)\)

\(\Rightarrow E=\frac{1}{2}.\frac{612}{1225}\)

\(\Rightarrow E=\frac{306}{1225}\)

Vậy...

b) \(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)

\(=\frac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=\frac{2.1}{1}=2\)

d) Bạn xem lại đề nhé