1.5+1.5

=5+5

=10

=10

các bạn cho mình vài li-ke cho tròn 545 với 

1.5+1.5

=5+5

=10

\(A=\frac{2}{1.5}+\frac{3}{5.11}+\frac{4}{11.19}+\frac{5}{19.29}+\frac{6}{29.41}\)

\(A=\frac{1}{2}\left(\frac{4}{1.5}+\frac{6}{5.11}+\frac{8}{11.19}+\frac{10}{19.29}+\frac{12}{29.41}\right)\)

\(A=\frac{1}{2}\left(\frac{5-1}{1.5}+\frac{11-5}{5.11}+\frac{19-11}{11.19}+\frac{29-19}{19.29}+\frac{41-29}{29.41}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{19}+\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{41}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{41}\right)=\frac{20}{41}\)

Đặt \(A=\dfrac{2}{1.5}+\dfrac{3}{5.11}+\dfrac{4}{11.19}+\dfrac{5}{19.29}+\dfrac{6}{29.41}\)

\(2A=\dfrac{4}{1.5}+\dfrac{6}{5.11}+\dfrac{8}{11.19}+\dfrac{10}{19.29}+\dfrac{12}{29.41}\)

\(2A=\dfrac{1}{1}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{41}\)

\(2A=\dfrac{1}{1}-\dfrac{1}{41}=\dfrac{40}{41}\)

\(A=\dfrac{40}{41}:2=\dfrac{20}{41}\)

Đặt \(B=\dfrac{1}{1.4}+\dfrac{2}{4.10}+\dfrac{3}{10.19}+\dfrac{4}{19.31}\)

Tương tự ta dễ dàng tình đc:

\(B=\dfrac{10}{31}=\dfrac{20}{62}\)

Ta có: \(\dfrac{20}{41}< \dfrac{20}{62}\Rightarrow A< B\)

Vậy ........................

Chúc bn học tốt

Đặt A=2/1.5+3/5.11+...+6/29.41

B=1/1.4+2/4.10+3/10.19+4/19.31

2A=4/1.5+6/5.11/+...+12/29.41

2A=1-1/5+1/5-1/11+...+1/29-1/41

2A=1-1/41

2A=40/41

A=20/41

3B=3/1.4+6/4.10+9/10.19+12/19.31

3B=1-1/4+1/4-1/10+1/10-1/19+1/19-1/31

3B=1-1/31

3B=30/31

B=10/31

Vì 10/31<20/41 nên B<A

Giải:

Đặt \(A=\dfrac{2}{1.5}+\dfrac{3}{5.11}+\dfrac{4}{11.19}+\dfrac{5}{19.29}+\dfrac{6}{29.41}\) 

\(A=\left(\dfrac{4}{1.5}+\dfrac{6}{5.11}+\dfrac{8}{11.19}+\dfrac{10}{19.29}+\dfrac{12}{29.41}\right):2\) 

\(A=\left(\dfrac{1}{1}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{41}\right):2\) 

\(A=\left(\dfrac{1}{1}-\dfrac{1}{41}\right):2\) 

\(A=\dfrac{40}{41}:2\) 

\(A=\dfrac{20}{41}\) 

Đặt \(B=\dfrac{1}{1.4}+\dfrac{2}{4.10}+\dfrac{3}{10.19}+\dfrac{4}{19.31}\) 

\(B=\left(\dfrac{3}{1.4}+\dfrac{6}{4.10}+\dfrac{9}{10.19}+\dfrac{12}{19.31}\right):3\) 

\(B=\left(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{31}\right):3\) 

\(B=\left(\dfrac{1}{1}-\dfrac{1}{31}\right):3\) 

\(B=\dfrac{30}{31}:3\) 

\(B=\dfrac{10}{31}\) 

Vì \(\dfrac{20}{41}>\dfrac{10}{31}\) nên A>B

                     Ta có :

                     \(A=\frac{4}{1.5}+\frac{5}{5.10}+\frac{6}{10.16}+\frac{7}{16.23}+\frac{8}{23.31}+\frac{9}{31.40}\)

                    \(A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+\frac{1}{23}-\frac{1}{31}+\frac{1}{31}-\frac{1}{40}\)

                   \(A=1-\frac{1}{40}=\frac{39}{40}\)

                   Ủng hộ mk nha !!! ^_^

A = 4/1 x 5 + 4/5 x 9 + 4/9 x 13 + .... + 4/91 x 95 + 4/95 x 99

A = 1 - 1/5 + 1/5 -1/9 + 1/9 - 1/13 + .... + 1/91 - 1/95 + 1/95 - 1/99

A = 1 - 1/99

A = 98/99

B = 1/6 + 1/12 + 1/20 + ... + 1/132

B = 1/2 x 3 + 1/3 x 4 + 1/4 x 5 + ... + 1/11 x 12

B = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/11 - 1/12 

B = 1/2 - 1/12 

B = 5/12

1 + 1 x 5 : 5 

= 1 + 1 x 5 : 5

= 1 + 1 x 1

= 1 + 1

= 2

= 1+5:5

=1+1

=2

1+1x5:5=1+5:5=1+1=2