A = \(\frac{5}{2.4}+\frac{5}{4.6}+\frac{5}{6.8}+...+\frac{5}{2014.2016}\)

A = \(5.\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2014.2016}\right)\)

A = \(\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)

A = \(\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{2016}\right)\)

A = \(\frac{5}{2}.\frac{1007}{2016}=\frac{5035}{4032}\)

\(A=\frac{5}{2.4}+\frac{5}{4.6}+\frac{5}{6.8}+...+\frac{5}{2014.2016}\)

\(\Rightarrow\frac{2}{5}A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2014.2016}\)

\(\Rightarrow\frac{2}{5}A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2014}-\frac{1}{2016}\)

\(\Rightarrow\frac{2}{5}A=\frac{1}{2}-\frac{1}{2016}\)

\(\Rightarrow\frac{2}{5}A=\frac{1008}{2016}-\frac{1}{2016}\)

\(\Rightarrow\frac{2}{5}A=\frac{1007}{2016}\)

\(\Rightarrow A=\frac{1007}{2016}\div\frac{2}{5}\)

\(\Rightarrow A=\frac{1007}{2016}\times\frac{5}{2}\)

\(\Rightarrow A=\frac{5035}{4032}\)

\(C=\left(-1+\frac{1}{2}\right)\left(-1+\frac{1}{3}\right)\left(-1+\frac{1}{4}\right)...\left(-1+\frac{1}{2016}\right)\)

\(\Rightarrow C=\left(\frac{-2}{2}+\frac{1}{2}\right)\left(\frac{-3}{3}+\frac{1}{3}\right)\left(\frac{-4}{4}+\frac{1}{4}\right)...\left(\frac{-2016}{2016}+\frac{1}{2016}\right)\)

\(\Rightarrow C=\frac{-1}{2}.\frac{-2}{3}.\frac{-3}{4}...\frac{-2015}{2016}\)

\(\Rightarrow C=\frac{-1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2015}{2016}\)

\(\Rightarrow C=\frac{-1}{2016}\)

T = 1 -2 + 3 - 4 + 5 - .... +2015 - 2016 + 2017

T = (1 -2) + (3 - 4) + (5 - 6) +.......(2015 - 2016) + 2017

Mỗi nhóm có kết quả bằng  - 1 và số nhóm sẽ là: [(2016 - 1) + 1] : 2 = 1008

=> T = -1 x 1008 + 2017 = - 1008 + 2017 = 1009

T=1009

đúng 100% tick nha

nhin tren ghi vao cung doi k a con lau(nhung minh k rui)

\(S=1-2+3-4+5-6+...+2015-2016\)

\(S=\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+...+\left(2015-2016\right)\)

\(S=\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)

Dãy S có 2016 số =>Có 1008 cặp -1.

\(S=\left(-1\right).1008\)

\(\Rightarrow\)\(S=-1008\)

Tk mk nhé(nếu đúng)!Thank you!

S= (1-2)+(3-4)+...+(2015-2016)(có 1008 ch/số)

=-1+(-1)+...+(-1)(có 1008 ch/s 1 )

=-1.2008

=-1

la -1008

S = (1+3+5+...+2015) - (2+4+6+...+2016)

S = 1016064 - 1017072

S = -1008

Chúc bạn học tốt !!!!

S = -1008

A = (1-2-3+4)+(5-6-7+8)+.....+(2013-2014-2015+2016)

   = 0+0+.....+0

   = 0

Tk mk nha

Cách 1:
Xét số bị trừ, ta có:
(2/3 + 3/4 + 4/5 + ... + 2016/2017) x (1/2 + 2/3 + 3/4 + ... + 2015/2016)
= (2/3 + 3/4 + 4/5 + ... + 2015/2016 + 2016/2017) x (1/2 + 2/3 + 3/4 + ... + 2015/2016)
= (2/3 + 3/4 + 4/5 + ... + 2015/2016) x (1/2 + 2/3 + 3/4 + ... + 2015/2016) + 2016/2017 x (1/2 + 2/3 + 3/4 + ... + 2015/2016)
Xét số trừ, ta có: 
(1/2 + 2/3 + 3/4 + ... + 2016/2017) x (2/3 + 3/4 + 4/5 + ... + 2015/2016)
= (1/2 + 2/3 + 3/4 + ... + 2015/2016 + 2016/2017) x (2/3 + 3/4 + 4/5 + ... + 2015/2016)
= (1/2 + 2/3 + 3/4 + ... + 2015/2016) x (2/3 + 3/4 + 4/5 + ... + 2015/2016) + 2016/2017 x (2/3 +3/4 + 4/5 + ... + 2015/2016) =
Ta thấy số bị trừ và số trừ có số hạng giống nhau là:
(2/3 +3/4 + 4/5 + ... + 2015/2016) x (1/2 + 2/3 + 3/4 + ... + 2015/2016)
Nên phép trừ trên có thể viết lại:
2016/2017 x (1/2 + 2/3 + 3/4 + ... + 2015/2016) - 2016/2017 x (2/3 + 3/4 + 4/5 + ... + 2015/2016)
= 2016/2017 x [(1/2 + 2/3 + 3/4 + ... + 2015/2016) - (2/3 +3/4 + 4/5 + ... + 2015/2016)]
= 2016/2017 x 1/2
= 1008/2017

Cách 2:

Là 1008/2017 đó nha

Tính: (2/3 + 3/4 + 4/5 + ... + 2016/2017) x (1/2 + 2/3 + 3/4 + ... + 2015/2016) – (1/2 + 2/3 + 3/4 + ... + 2016/2017) x (2/3 + 3/4 + 4/5 + ... + 2015/2016).

\(B=2+2^2+2^3+...+2^{2016}\)

\(2B=2^2+2^3+...+2^{2017}\)

\(B=2^{2017}-2\)

các ý khác tương tự 

ý C nhân vs 3

   D                4

  E                5

3C = 3(1+3+3^2+.......+3^2017)

= 3+3^2+3^3+......+3^2018

3C - C = (3+3^2+3^3+......+3^2018) - (1+3+3^2+......+3^2017)

= 3^2018 - 1

=> C = (3^2018 - 1) : 2

còn lại tự làm nhé