Question

cho A=1+2012+2012^2+2012^3+.......+2012^100 và B=2012^101/2011. Tính B-A

Answer 1

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