\(y-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{12}-\dfrac{1}{20}-\dfrac{1}{30}-\dfrac{1}{42}=1\)

\(y-\dfrac{6}{7}=1\)

\(y=\dfrac{13}{7}\)

1/3 nhé

Ta có:

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(\Rightarrow\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)

1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42

= 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

= 1/1 + 1/7

= 8/7

Bằng \(\frac{9}{22}\)nha bạn.

\(\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{10.11}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-......+\frac{1}{10}-\frac{1}{11}.\)

=\(\frac{1}{2}-\frac{1}{11}\)

=\(\frac{9}{22}.\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}=\frac{5}{6}\)

1/2 + 5/6 + 11/12 + 19/20 + 29/30 = 16/5

16/5 đó bạn.

k cho mình nha mấy bạn cao điểm

Chú ý \(.\)là dấu nhân .

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\)\(\frac{1}{90}\)

=\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+_{\text{ }}\)\(\frac{1}{9.10}\)

= \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\)\(\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\)

= \(\frac{1}{2}-\frac{1}{10}\)

=\(\frac{2}{5}\)

Vì tử số bé hơn mẫu số nên phân số \(\frac{2}{5}\)< 1

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=1-\frac{1}{7}=\frac{7-1}{7}=\frac{6}{7}\)