a: =>x-2/5=3/4:1/3=3/4*3=9/4

=>x=9/4+2/5=45/20+8/20=53/20

b: =>x-2/3=7/3:4/5=7/3*5/4=35/12

=>x=35/12+2/3=43/12

c: 1/3(x-2/5)=4/5

=>x-2/5=4/5*3=12/5

=>x=12/5+2/5=14/5

d: =>2/3x-1/3-1/4x+1/10=7/3

=>5/12x-7/30=7/3

=>5/12x=7/3+7/30=77/30

=>x=77/30:5/12=154/25

e: \(\Leftrightarrow x\cdot\dfrac{3}{7}-\dfrac{2}{7}+\dfrac{1}{2}-\dfrac{5}{4}x+\dfrac{5}{2}=0\)

=>\(x\cdot\dfrac{-23}{28}=\dfrac{2}{7}-3=\dfrac{-19}{7}\)

=>x=19/7:23/28=76/23

f: =>1/2x-3/2+1/3x-4/3+1/4x-5/4=1/5

=>13/12x=1/5+3/2+4/3+5/4=257/60

=>x=257/65

i: =>x^2-2/5x-x^2-2x+11/4=4/3

=>-12/5x=4/3-11/4=-17/12

=>x=17/12:12/5=85/144

??????????????????????????????????????????????

Lần đầu post, mình quên mất chưa nêu câu hỏi. Nhờ các bạn chứng minh dùm 3 câu trên với, cám ơn nhiều ah!

7

14

21

28

30

= 7 

= 14

= 21

= 28

= 30

a) = 1/2 - 1/2 + 1/3 -1/3 + 1/4 - 1/4 + 1/5 - 1/5 + 1/6

    =  0 + 0 + 0 + 0 + 1/6

    = 1/6

b) 2/3 + 2/4 - 2/4 + 2/5 - 2/5 + 2/6 - 2/6 + 2/7 - 2/7 + 28

=  2/3 + 28

=     86/3

[tick cho mik nha]

Kho..................wa.....................troi.....................thi......................lanh.................ret.......................ai........................tich..........................ung.....................ho........................minh.....................cho....................do....................lanh

\(7832\)

Lời giải chi tiết:

\(B=1+5+5^2+5^3+...+5^{2008}+5^{2009}\)

\(\Rightarrow 5B=5+5^2+5^3+5^4+...+5^{2009}+5^{2010}\)

Trừ theo vế:

\(5B-B=(5+5^2+5^3+5^4+...+5^{2009}+5^{2010})-(1+5+5^2+...+5^{2009})\)

\(4B=5^{2010}-1\)

\(B=\frac{5^{2010}-1}{4}\)

\(S=\frac{3^0+1}{2}+\frac{3^1+1}{2}+\frac{3^2+1}{2}+..+\frac{3^{n-1}+1}{2}\)

\(=\frac{3^0+3^1+3^2+...+3^{n-1}}{2}+\frac{\underbrace{1+1+...+1}_{n}}{2}\)

\(=\frac{3^0+3^1+3^2+..+3^{n-1}}{2}+\frac{n}{2}\)

Đặt \(X=3^0+3^1+3^2+..+3^{n-1}\)

\(\Rightarrow 3X=3^1+3^2+3^3+...+3^{n}\)

Trừ theo vế:

\(3X-X=3^n-3^0=3^n-1\)

\(\Rightarrow X=\frac{3^n-1}{2}\). Do đó \(S=\frac{3^n-1}{4}+\frac{n}{2}\)

Lời giải chi tiết: