3.

\(A=1-3+3^2-3^3+...-3^{2009}-3^{2010}\)

\(\Rightarrow3A=3-3^2+3^3-3^4+...-3^{2010}+3^{2011}\)

\(\Rightarrow4A=3-3^2+3^3-3^4+...-3^{2010}+3^{2011}+\left(1-3+3^2-3^3+...-3^{2009}+3^{2010}\right)\)\(\Rightarrow4A=3^{2011}-1\)

\(\Rightarrow4A=3^{2011}\)

\(\Rightarrow\)ĐPCM

3 hostages have been kept by this terrorist for a week

I will be picked up at my house by my father

 I will be taken to HCMC next week by my father

31.3 hostages have been hept by this terrorist for a week

32.I will be picked up at my house by them

33.I will be taken to Ho Chi Minh city by my father next week.

Chúc em học tốt

31.3 hostages were held by the terrorist in a week.

32.I will be picked up by them at my house.

33.I will be brought to HCMC by my father next week.

2010-0=2010:10+1=202

Đơn thức A=-3 nên có gt âm

nếu x và y khác 0 (trường hợp âm)=> B nhận gt âm

nếu x và y bằng 0 thì C nhận gt bằng 0

chtt ! tick minh nha ban

Vì : a/b=c/d nên =>a/c=b/d

Đặt: a/c=b/d=k thì =>a=ck;b=dk

Thay :a=ck và b=dk vào 2a-3b/4a+5b có : 

2a-3b/4a+5b=2ck-3dk/4ck+5dk=k(2c-3d)/k(4c+5d)=2c-3d/4c+5d

Tu đây suy ra : 2a-3b/4a+5b=2c-3d/4c+5d

****

Ta có: \(A=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}=1-\frac{1}{100}=\frac{99}{100}< 1\)

Vậy A<1

Học tốt nha!!!

Ta có :

\(C=4+2^2+2^3+...+2^{2016}\)

\(\Rightarrow C-4=2^2+2^3+...+2^{2016}\)

\(\Rightarrow2\left(C-4\right)=2^3+2^4+...+2^{2017}\)

\(\Rightarrow2\left(C-4\right)-\left(C-4\right)=\left(2^3+2^4+...+2^{2017}\right)-\left(2^2+2^3+...+2^{2016}\right)\)

\(\Rightarrow C-4=2^{2017}-2^2\)

\(\Rightarrow C=2^{2017}\)

=> Đpcm

C= 4 + 2^2 + 2^3 + 2^4 +.....+2^2016

Đặt A=  2^2 + 2^3 + 2^4 +.....+2^2016

=>2A= 2^3 + 2^4 +2^5.....+2^2017

=>2A-A= 2^2017 - 2^2 = 2^2017 - 4

=>C= 4+A= 4+2^2017 - 4

=>C=2^2017

Vậy C là lũy thừa của 2 

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