Tính nhanh: 4/9+4/45+4/105+4/189
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\(\frac{4}{9}+\frac{4}{45}+\frac{4}{105}+\frac{4}{189}\)
\(=\frac{8}{15}+\frac{4}{105}+\frac{4}{189}\)
\(=\frac{4}{7}+\frac{4}{189}\)
\(=\frac{16}{27}\)
Học tốt #
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Bạn tải photomath về là giải được ngay !
Nhớ k cho mình nhé !
Gọi biểu thức này là A
Ta có :
\(A=\frac{4}{45}+\frac{4}{105}+\frac{4}{189}+\frac{4}{297}+\frac{4}{929}\)
\(\frac{3}{2}A=\frac{3}{2}\times\left(\frac{4}{45}+\frac{4}{105}+\frac{4}{189}+\frac{4}{297}+\frac{4}{929}\right)\)
\(\frac{3}{2}A=\frac{6}{45}+\frac{6}{105}+\frac{6}{189}+\frac{6}{297}+\frac{6}{929}\)
\(\frac{3}{2}A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{???}\)
Bạn nên xem lại bài
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#)Giải :
\(\frac{1}{15}+\frac{4}{30}+\frac{9}{45}+\frac{16}{60}+...+\frac{81}{135}=\frac{1}{15}+\frac{2}{15}+\frac{3}{15}+...+\frac{9}{15}=\frac{45}{15}=3\)
Dễ ẹc ak :v rút gọn là ra
=(\(\frac{1}{15}\)+\(\frac{4}{30}\)+\(\frac{16}{60}\)+\(\frac{64}{120}\))+(\(\frac{9}{45}\)+\(\frac{36}{90}\))+(\(\frac{25}{75}\)+\(\frac{81}{135}\))
=(\(\frac{8}{120}\)+\(\frac{16}{120}\)+\(\frac{32}{120}\)+\(\frac{64}{120}\))+(\(\frac{18}{90}\)+\(\frac{36}{90}\))+\(\frac{14}{15}\).
=1+\(\frac{3}{5}\)+\(\frac{14}{15}\).
=\(\frac{8}{5}\)+\(\frac{14}{15}\).
=\(\frac{15}{38}\)
A = \(\dfrac{4}{9}\)+ \(\dfrac{4}{45}\)+ \(\dfrac{4}{105}\)+ \(\dfrac{4}{189}\)
A = \(\dfrac{2}{3}\)( \(\dfrac{2}{3}\)+ \(\dfrac{2}{15}\)+ \(\dfrac{2}{35}\)+ \(\dfrac{2}{63}\))
A = \(\dfrac{2}{3}\)(\(\dfrac{2}{1.3}\)+ \(\dfrac{2}{3.5}\)+ \(\dfrac{2}{5.7}\)+ \(\dfrac{2}{7.9}\))
A = \(\dfrac{2}{3}\)( 1- \(\dfrac{1}{3}\)+ \(\dfrac{1}{3}\)- \(\dfrac{1}{5}\)+ \(\dfrac{1}{5}\)- \(\dfrac{1}{7}\)+ \(\dfrac{1}{7}\)- \(\dfrac{1}{9}\))
A = \(\dfrac{2}{3}\)(1 - \(\dfrac{1}{9}\))
A = \(\dfrac{2}{3}\). \(\dfrac{8}{9}\)
A = \(\dfrac{16}{27}\)
dấu . là dấu nhân bạn nhé