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

Ta có; \(S=2012+\frac{2012}{1+2}+\frac{2012}{1+2+3}+\cdots+\frac{2012}{1+2+\cdots+2011}\)

\(=2012+\frac{2012}{2\cdot\frac32}+\frac{2012}{3\cdot\frac42}+\cdots+\frac{2012}{2011\cdot\frac{2012}{2}}\)

\(=2012+2\left(\frac{2012}{2\cdot3}+\frac{2012}{3\cdot4}+\cdots+\frac{2012}{2011\cdot2012}\right)\)

\(=2012+4024\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\cdots+\frac{1}{2011\cdot2012}\right)\)

\(=2012+4024\left(\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{2011}-\frac{1}{2012}\right)\)

\(=2012+4024\left(\frac12-\frac{1}{2012}\right)=2012+2012-2=4024-2=4022\)

A = 1 + 2012 + 2012² + ... + 2012¹⁰⁰

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

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

2011A = 2012¹⁰¹ - 1

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

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

thank bạn