Nhầm !!!!!

\(B-A=\frac{2012^{101}}{2011}-\frac{2012^{101}-1}{2011}=\frac{2012^{101}-\left(2012^{101}-1\right)}{2011}=\frac{1}{2011}\)

OK NHA

ai nhanh nhat dc 3 k nha

2012A = 2012(1 + 2012 + 2012² + .... + 2012¹⁰⁰)

= 2012 + 2012² + 2012³ + .... + 2012¹⁰¹

2012A - A = ( 2012 + 2012² + 2012³ + .... + 2012¹⁰¹) - (1 + 2012 + 2012² + .... + 2012¹⁰⁰)

2011A = 2012¹⁰¹ - 1

=> A = (2012¹⁰¹ - 1)/3

Vì (2012¹⁰¹ - 1)/2011 < 2012¹⁰¹/2011

=> A < B

Ta có :

\(A=1+2012+2012^2+2012^3+........+2012^{100}\)

\(2012A=2012+2012^2+2012^3+......+2012^{100}+2012^{101}\)

\(\Rightarrow2012A-A=\left(2012+2012^2+.......+2012^{101}\right)-\left(1+2012+........+2012^{100}\right)\)

\(2011A=2012^{101}-1\)

\(\Rightarrow A=\dfrac{2012^{101}-1}{11}\)

Mà \(B=\dfrac{2012^{101}}{2011}\)

\(\Rightarrow B-A=\dfrac{2012^{101}}{2011}-\dfrac{2012^{101}-1}{2011}\)

\(=\dfrac{2012^{101}-\left(2012^{101}-1\right)}{2011}\)

\(=\dfrac{2012^{101}-2012^{101}+1}{2011}\)

\(=\dfrac{1}{2011}\)

~ Chúc bn học tốt ~

Có: \(2012A=2012+2012^2+...+2012^{101}\)
=> \(2012A-A=\left(2012+2012^2+...+2012^{101}\right)-\left(1+2012+...+2012^{100}\right)\)
\(\Rightarrow2011A=2012^{101}-1\)
\(\Rightarrow A=\dfrac{2012^{101}-1}{2011}\)
Do đó \(B-A=\dfrac{2012^{101}}{2011}-\dfrac{2012^{101}-1}{2011}=\dfrac{1}{2011}\)

\(B=1+2012+2012^2+2012^3+...+2012^{100}\)

2012B= 2012 + 2012^2 + 2012^3 + ... + 2012^101

2012B - B = (2012 + 2012^2 + 2012^3 + ... + 2012^101) - (1+ 2012 + 2012^2 + ...+ 2012^100)

2011B = 2012^101 - 1

B = \(\frac{2012^{101}-1}{2011}\)

=> C - B = \(\frac{2012^{101}}{2011}-\frac{2012^{101}-1}{2011}=\frac{2012^{101}-\left(2012^{101}-1\right)}{2011}\)\(=\frac{2012^{101}-2012^{101}+1}{2011}=\frac{1}{2011}\)

lầm sau đừng viết chữ to chữ nhỏ nữa nhe oOo _ Virgo _ oOo ^_^^_^^_^

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