6+6.9+6.92+6.93+..............+6.999
\(=6.\left(1+9+9^2+9^3+...........+9^{99}\right)\)
Đặt A=1+9+92+93+........+999
\(\Rightarrow9A=9+9^2+9^3+9^4+.....+9^{100}\)
\(\Rightarrow9A-A=\left(9+9^2+9^3+9^4+.....+9^{100}\right)-\left(1+9+9^2+9^3+............+9^{99}\right)\)
\(\Rightarrow8A=9^{100}-1\)
\(\Rightarrow A=\frac{9^{100}-1}{8}\)
+)Thay A vào \(6.\left(1+9+9^2+9^3+...........+9^{99}\right)\)được:
\(=6.\frac{9^{100}-1}{8}=\frac{54^{100}-6}{8}\)
Chúc bn học tốt