Question

Tính 

V=\(4.5^{100}.\left(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\right)+1\)1

Answer 1

bạn viết rõ được ko

Answer 2

mình viết thừa số 1 ở cuối nhé

Answer 3

Đặt \(A=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+....+\frac{1}{5^{100}}\)

\(5A=5+\frac{1}{5}+\frac{1}{5^2}+....+\frac{1}{5^{99}}\)

\(5A-A=1-\frac{1}{5^{100}}\)

\(4A=1-\frac{1}{5^{100}}\)

\(A=\frac{1-\frac{1}{5^{100}}}{4}\)

\(A=\frac{1}{4}-\frac{1}{4.5^{100}}\)

\(V=4.5^{100}\left(\frac{1}{4}_{ }-\frac{1}{4.5^{100}}\right)+1\)

\(V=\left(4.5^{100}.\frac{1}{4}-4.5^{100}.\frac{1}{4.5^{100}}\right)+1\)

\(V=\left(5^{100}-1\right)+1\)

\(V=5^{100}\)