\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{15}-\dfrac{1}{18}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{18}\right)=\dfrac{1}{3}\cdot\dfrac{5}{18}=\dfrac{5}{54}\)

\(\dfrac{5}{54}\)

đúng rồi đó

rồi,kp nha

Đặt A =4/1x3 + 6/3x6+8/6x10 +14/10x17 +12/17x23 . => A/2 = 2/1x3 +3/3x6 +4/6x10+7/10x17 +6/17x23. =>A/2 = 1-1/3 + 1/3-1/6+1/6-1/10+1/10-1/17+1/17-1/23. => A/2=1-1/23 . => A/2=22/23 . => A=44/23 . cho mik nha

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\(A=\frac{4}{1.3}+\frac{6}{3.6}+\frac{8}{6.10}+\frac{14}{10.17}+\frac{12}{17.23}\)

\(=2\left(\frac{2}{1.3}+\frac{3}{3.6}+\frac{4}{6.10}+\frac{7}{10.17}+\frac{6}{17.23}\right)\)

\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{17}+\frac{1}{17}-\frac{1}{23}\right)\)

\(=2\left(1-\frac{1}{23}\right)\)

\(=2\cdot\frac{22}{23}=\frac{44}{23}\)

\(N=\dfrac{2}{3.6}+\dfrac{2}{6.9}+...+\dfrac{2}{2019.2022}\)

\(\Rightarrow N=2\left(\dfrac{1}{3.6}+\dfrac{1}{6.9}+...+\dfrac{1}{2019.2022}\right)\)

\(\Rightarrow N=\dfrac{2}{3}\left(\dfrac{3}{3.6}+\dfrac{3}{6.9}+...+\dfrac{3}{2019.2022}\right)\)

\(\Rightarrow N=\dfrac{2}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{2019}-\dfrac{1}{2022}\right)\)

\(\Rightarrow N=\dfrac{2}{3}\left(\dfrac{1}{3}-\dfrac{1}{2022}\right)\)

\(\Rightarrow N=\dfrac{2}{3}.\dfrac{673}{2022}\\ \Rightarrow N=\dfrac{673}{3033}\)

a,6B=2.4.6+4.6.(8-2)+...............+98.100.(102-96)

6B=2.4.6+4.6.8-2.4.6+..............+98.100.102-96.98.100

6B=98.100.102

B=98.100.102:6

B=166600

giúp mk với

bài này khó quá!

giúp nha

thanks

Đầu tiên ta rút gọn \(\frac{4^{^6}.9^{^5}+6^{^9}.120}{8^{^4}.3^{^{12}}-6^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}+2^{^9}.3^{^9}.2^{^3}.3.5}{2^{^{12}}.3^{^{12}}-2^{^{11}}-3^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}+2^{^{12}}.3^{^{10}}.5}{2^{^{12}}.3^{^{12}}-2^{^{11}}.3^{^{11}}}\)= \(\frac{2^{^{12}}.3^{^{10}}.\left(1+5\right)}{2^{^{11}}.3^{^{11}}.\left(6-1\right)}\)= \(\frac{2.6}{3.5}\)= \(\frac{12}{15}\)= \(\frac{4}{5}\)

\(\Rightarrow\)10 . \(\frac{4}{5}\)= \(\frac{40}{5}\)= 8