Question

[công chúa giá băng]

thu gon

a.A=43+6^3+6^4+6^5+...+6^99+6^100

b.Tính B=A-6^101

Answer 1

[Trần Phúc]

Ta có:

\(A=43+6^3+6^4+6^5+...+6^{99}+6^{100}\)

\(\Rightarrow6A=6^0+6^1+6^2+6^3+6^4+6^5+...+6^{99}+6^{100}\)

\(\Rightarrow6A-A=\left(6+6^2+6^3+6^4+...+6^{101}\right)-\left(1+6+6^2+6^3+...+6^{100}\right)\)

\(\Rightarrow A.\left(6-1\right)=6^{101}-1\Leftrightarrow A=\frac{6^{101}-1}{6-1}\)

b) \(B=A-6^{101}\)

\(\Rightarrow B=\frac{6^{101}-1}{6-1}-6^{101}\)