Question

tính nhanh:   \(\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{61.66}\)

Answer 1

\(\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{61.66}\)

=\(\frac{1}{5}.\frac{5}{11.16}+\frac{1}{5}.\frac{5}{16.21}+\frac{1}{5}.\frac{5}{21.26}+...+\frac{1}{5}.\frac{5}{61.66}\)

=\(\frac{1}{5}.\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\right)\)

=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

=\(\frac{1}{5}.\left(\frac{6}{66}-\frac{1}{66}\right)=\frac{1}{5}.\frac{5}{66}=\frac{1}{66}\)

Answer 2

Đặt A = \(\frac{1}{11.16}+...+\frac{1}{61.66}\)

 

5A    = \(\frac{5}{11.16}+..+\frac{5}{61.66}\)

5a    = \(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)

5a   =  \(\frac{1}{11}-\frac{1}{61}\)

5a   =  50/671

a     = \(\frac{50}{671}:5=\frac{10}{671}\)

Answer 3

\(\frac{1}{11.16}+\frac{1}{16.21}\)\(+\frac{1}{21.26}+...+\frac{1}{61.66}\)

= \(\frac{1}{5}.\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)

= \(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

= \(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

= \(\frac{1}{5}.\left(\frac{5}{6}\right)\)

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

k mk nha !

Answer 4

Mk nhầm . Đoạn cuối mình xin làm lại là :

\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

= \(\frac{1}{5}.\left(\frac{5}{66}\right)\)

= \(\frac{1}{66}\)

Rồi k mk nha !

Answer 5

\(\frac{1}{5}\).(\(\frac{1}{11}\)-\(\frac{1}{16}\)+\(\frac{1}{16}-\frac{1}{21}+......+\)\(\frac{1}{61}-\frac{1}{66}\))

\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

tính trong ngoặc rồi nhân ok

Answer 6

Đặt A = \(\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{61.66}\)

\(\Rightarrow5A=\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)

\(5A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)

\(5A=\frac{1}{11}-\frac{1}{66}\)

\(5A=\frac{5}{66}\Rightarrow A=\frac{5}{66}:5=\frac{1}{66}\)

Answer 7

\(\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{61.66}\)

\(=\frac{1}{5}.\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)

\(=\frac{1}{5}.\left(\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{61.66}\right)\)

\(=\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{1}{5}.\frac{5}{66}\)

\(=\frac{1}{66}\)