Question

a,\(A=1+5+5^2+5^3+...+5^{2014}+5^{2015}\)

b,\(B=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

           giải rõ giùm nghen

Answer 1

a, \(A=1+5+5^2+5^3+....+5^{2014}+5^{2015}\Rightarrow5A=5+5^2+5^3+5^4+.....+5^{2015}+5^{2016}\)

\(\Rightarrow5A-A=\left(5+5^2+5^3+....+5^{2015}+5^{2016}\right)-\left(1+5+5^2+.....+5^{2014}+5^{2015}\right)\)

\(\Rightarrow4A=5^{2016}-1\Rightarrow A=\frac{5^{2016}-1}{4}\)

b,\(B=2^{100}-2^{99}+2^{98}-.....-2^3+2^2-2\Rightarrow2B=2^{101}-2^{100}+2^{99}-.....-2^4+2^3-2^2\)

\(\Rightarrow B+2B=\left(2^{101}-2^{100}+2^{99}-.....-2^4+2^3-2^2\right)+\left(2^{100}-2^{99}+2^{98}-.....-2^3+2^2-2\right)\)

\(\Rightarrow3B=2^{101}-2\Rightarrow B=\frac{2^{101}-2}{3}\)

Answer 2

`4`