Question

Rút gọn.

\(A=5+5^2+5^3+...+5^{101}\)

Answer 1

\(5A=5^2+5^3+....+5^{102}\)

\(\Rightarrow5A-A=4A=\left(5^2+5^3+....+5^{102}\right)-\left(5+5^2+.....+5^{102}\right)\)

\(\Rightarrow4A=5^{102}-5\)

\(\Rightarrow A=\frac{5^{102}-5}{4}\)

Answer 2

Ta có:

\(A=5+5^2+5^3+...+5^{101}\)

\(\Rightarrow5.A=5^2+5^3+5^4+...+5^{102}\)

\(\Rightarrow5.A-A=\left(5^2+5^3+5^4+...+5^{102}\right)-\left(5+5^2+5^3+...+5^{101}\right)\)

\(\Rightarrow4.A=5^{102}-5\)

\(\Rightarrow A=\left(5^{102}-5\right):4\)

Answer 3

\(A=5+5^2+5^3+5^4+....+5^{99}+5^{100}\)

\(5B=5^2+5^3+5^4+5^5+...+5^{501}\)

\(5B-B=5^2+5^3+...+5^{101}-5-5^2-5^3-....-5^{99}-5^{100}\)

\(4B=5^2+5^3+5^4+....+5^{100}+5^{101}-\left(5+5^2+5^3+...+5^{99}+5^{100}\right)\)

\(4B=5^{101}-5\)

\(\Rightarrow B=\left(5^{101}-5\right):4\)

Answer 4

Hai người copy y chang nhau