=14

k mik nha

1 x 2 + 1 x 3 + 1 x 4 + 1 x 5

= 2 + 3 + 4 + 5

= 6 + 4 + 5

= 10 + 5

= 15

= 2 + 3 + 4 + 5

= 14

nhé

\(\frac{149}{60}\)

k mk nha mk đag âm

\(\frac{1}{1\times2}\) + \(\frac{1}{1\times3}\) + \(\frac{1}{1\times4}\) + \(\frac{1}{1\times5}\) + \(\frac{12}{10}\)

= \(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) + \(\frac{1}{5}\) + \(\frac{12}{10}\)

= \(\frac{149}{60}\)

\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{12}{10}\)

\(A=\frac{30}{60}+\frac{20}{60}+\frac{15}{60}+\frac{12}{60}+\frac{72}{60}\)

\(A=\frac{30+20+15+12+72}{60}\)

\(A=\frac{149}{60}\)

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\(a,\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{43.45}=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{43.45}\right)=\frac{5}{3}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{45}\right)=\frac{5}{3}.\frac{44}{45}=\frac{44}{27}\)

Sửa đề tí :

\(S=\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+...+\frac{3}{2013\cdot2015}\)

\(S=\frac{3}{2}\left[\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{2013\cdot2015}\right]\)

\(S=\frac{3}{2}\left[1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2013}-\frac{1}{2015}\right]\)

\(S=\frac{3}{2}\left[1-\frac{1}{2015}\right]=\frac{3}{2}\cdot\frac{2014}{2015}=\frac{3021}{2015}\)

Ta có : S = 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 +......+1/2013-1/2015

 Ta gạch các phân số ở giữa còn lại 1/1 - 1/2015=2014/2015

Vậy S = 2014/2015 

K 2 LẦN NHÉ

OK CHƯA

M = 3/1x3 + 3/3x5 + 3/5x7 + ... + 3/45x47 + 3/47x49

M = 3/2 x (2/1x3 + 2/3x5 + 2/5x7 + ... + 2/45x47 + 2/47x49)

M = 3/2 x (1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/45 - 1/47 + 1/47 - 1/49)

M = 3/2 x (1 - 1/49)

M = 3/2 x 48/49

M = 72/49

N tính tương tự, nhân N với 5/4 

Nhanh nha mình cần gấp 

ghi cả cách trình bày ra nhé

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