Question

ai tính hộ tui với

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\(\frac{1}{2\cdot6}+\frac{1}{4\cdot9}+\frac{1}{6\cdot12}+...+\frac{1}{36\cdot57}+\frac{1}{38\cdot60}\) 

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Answer 1

Ta có:\(\frac{1}{2\times6}+\frac{1}{4\times9}+...+\frac{1}{36\times57}+\frac{1}{38\times60}\)

       \(=\frac{1}{6}\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{18\times19}+\frac{1}{19\times20}\right)\)

       \(=\frac{1}{6}\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

       \(=\frac{1}{6}\times\left(1-\frac{1}{20}\right)\)

       \(=\frac{1}{6}\times\frac{19}{20}=\frac{19}{120}\)

(đây chắc là toán lớp 7,bạn ạ)

Answer 2

Đặt A= 1/2.6 + 1/4.9 + 1/6.12 + ... + 1/36.57 + 1/38.60

A= 1/2.1.2.3 + 1/2.2.3.3 + 1/2.3.3.4 + ... + 1/2.18.3.19 + 1/2.19.3.20

A= 1/1.2.6 + 1/2.3.6 + 1/3.4.6 + ... + 1/18.19.6 + 1/19.20.6

A= 1/6 . ( 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/18.19 + 1/19.20)

A= 1/6 . ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/18 - 1/19 + 1/19 - 1/20)

A= 1/6 . ( 1-1/20)

A= 1/6 . 19/20

A= 19/120

Answer 3

Đặt A= 1/2.6 + 1/4.9 + 1/6.12 + ... + 1/36.57 + 1/38.60

A= 1/2.1.2.3 + 1/2.2.3.3 + 1/2.3.3.4 + ... + 1/2.18.3.19 + 1/2.19.3.20

A= 1/1.2.6 + 1/2.3.6 + 1/3.4.6 + ... + 1/18.19.6 + 1/19.20.6

A= 1/6 . ( 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/18.19 + 1/19.20)

A= 1/6 . ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/18 - 1/19 + 1/19 - 1/20)

A= 1/6 . ( 1-1/20)

A= 1/6 . 19/20

A= 19/120

Answer 4

19/120

Answer 5

19/120

Answer 6

\(\frac{1}{2x6}+\frac{1}{4x9}+\frac{1}{6x12}+...+\frac{1}{36x57}+\frac{1}{38x60}\)

=\(\frac{1}{6}x\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

=\(\frac{1}{6}x\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(\frac{1}{6}x\frac{19}{20}\)

=\(\frac{19}{120}\)

Answer 7

ta có \(\frac{1}{2.6}+\frac{1}{4.9}+...+\frac{1}{38.60}=\frac{1}{6}.\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{380}\right)\)

                                                                        = \(\frac{1}{6}\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{19.20}\right)\)

                                                                       =1/6.(1/1-1/2+1/2-1/3+....+1/19-1/20)

                                                                       =1/6(1-1/20)=1/6 . 19/20=19/120

Answer 8

19/120

Answer 9

\(\frac{1}{2\cdot6}+\frac{1}{4\cdot9}+...+\frac{1}{36\cdot57}+\frac{1}{38\cdot60}\)

\(=\frac{1}{6}\cdot\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{18\cdot19}+\frac{1}{19\cdot20}\right)\)

\(=\frac{1}{6}\cdot\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(=\frac{1}{6}\cdot\left(1-\frac{1}{20}\right)\)

\(=\frac{1}{6}\cdot\frac{19}{20}=\frac{19}{120}\)