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\(\left(1^1+2^2+3^3+4^4+...+2022^{2022}\right)\left(8^2-576:3^2\right)\)
\(=\left(1^1+2^2+3^3+4^4+...+2022^{2022}\right)\left(64-576:3^2\right)\)
\(=\left(1^1+2^2+3^3+4^4+...+2022^{2022}\right)\left(64-64\right)\)
\(=\left(1^1+2^2+3^3+4^4+2022^{2022}\right).0\)
\(=0\)
ta có A=\(\dfrac{6}{8}\)+\(\dfrac{6}{56}\)+\(\dfrac{6}{140}\)+...+\(\dfrac{6}{1100}\)+\(\dfrac{6}{1400}\)
=\(\dfrac{3}{4}\)+\(\dfrac{3}{28}\)+\(\dfrac{3}{70}\)+...+\(\dfrac{3}{550}\)+\(\dfrac{3}{700}\)
=\(\dfrac{3}{1.4}\)+\(\dfrac{3}{4.7}\)+\(\dfrac{3}{7.10}\)+...+\(\dfrac{3}{22.25}\)+\(\dfrac{3}{25.28}\)
=1-\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{10}\)+...+\(\dfrac{1}{22}\)-\(\dfrac{1}{25}\)+\(\dfrac{1}{25}\)-\(\dfrac{1}{28}\)
=1-\(\dfrac{1}{28}\)
=\(\dfrac{27}{28}\)
Vậy A=\(\dfrac{27}{28}\)
Ta có:
A =6/8+6/56+6/140+...+6/1100+6/1400
⇒A=3/4+3/28+3/70+...+3/550+3/700
⇒A=3/1.4+3/4.7+3/7.10+...+3/22.25+3/25.28
⇒A=1−1/4+1/4−1/7+1/7−1/10+...+1/22−1/25+1/25−1/28
⇒A=1−1/28
⇒A=1-1/38
Với $x=1$ ta có :
$-7.(x+3)^3 .|2x-1|+42$
$=-7.(-1+3)^3.|2.(-1)-1|+42$
$=-7.2^3.|-3|+42$
$=-7.8.3 + 42$
$=-126$
\(=\frac{4}{28}+\frac{4}{70}+\frac{4}{130}+....+\frac{4}{550}=\frac{4}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{22.25}\right)\)
\(=\frac{4}{3}.\left(\frac{7-4}{4.7}+\frac{10-7}{7.10}+\frac{13-10}{10.13}+...+\frac{25-22}{22.25}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{22}-\frac{1}{25}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{4}-\frac{1}{25}\right)=\frac{4}{3}.\frac{21}{100}=\frac{7}{25}\)
\(\frac{8}{56}+\frac{8}{140}+\frac{8}{260}+...+\frac{8}{1400}=\frac{4}{28}+\frac{4}{70}+\frac{4}{130}+...+\frac{4}{700}\)
\(=\frac{4}{4.7}+\frac{4}{7.10}+\frac{4}{10.13}+...+\frac{4}{25.28}\)
\(=\frac{4}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)
\(=\frac{4}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{4}{3}\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{4}{3}.\frac{3}{14}=\frac{2}{7}\)