Question

100 trên 3 + 100 trên 3 mũ 2 +100 trên 3 mũ 3 +100 trên 3 mũ 4

ai mhanh minh k

Answer 1

\(\frac{4000}{81}\)

Answer 2

đặt \(A=\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}+\frac{100}{3^4}\)

\(3A=100+\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}\)

\(3A-A=100-\frac{100}{3^4}\) hay \(2A=100-\frac{100}{3^4}\)

\(A=\frac{100-\frac{100}{3^4}}{2}\)

Answer 3

Gọi \(A=\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}+\frac{100}{3^4}\)

\(3A=100+\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}\)

\(3A-A=\left(100+\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}\right)-\left(\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}+\frac{100}{3^4}\right)\)

\(2A=100-\frac{100}{3^4}\)

\(A=\frac{100-\frac{100}{3^4}}{2}\)

Answer 4

\(\frac{100}{3}+\frac{100}{3^2}+\frac{100}{3^3}+\frac{100}{3^4}\)

\(=\frac{100}{3}.\left(\frac{3}{3}+\frac{3}{3^2}+\frac{3}{3^3}+\frac{3}{3^3}\right)\)

\(=\frac{100}{3}.\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}\right)\)

Đặt A=\(\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}\right)\)

ta có:

\(3A=3+1+\frac{1}{3}+\frac{1}{3^2}\)

\(2A=\left(3+1+\frac{1}{3}+\frac{1}{3^2}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}\right)\)

\(2A=3-\frac{1}{3^3}\)

=> ....