Question

Cho A = 5+5²+......+5¹⁰⁰

a, Tinh A

b, A la so nguyen to hay hop so ?

c, A co la so chinh phuong ko

 

Answer 1

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

\(\Rightarrow5A-A=4A=\left(5^2+5^3+...+5^{101}\right)-\left(5+5^2+...+5^{100}\right)\)

\(\Rightarrow4A=5^{101}-5\)

\(\Rightarrow A=\frac{5^{101}-5}{4}\)

mấy cái còn lại tự làm nha mới nằm viện về ko sung sức lắm :)

Answer 2

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

\(\Rightarrow5A=5\left(5+5^2+...+5^{100}\right)=5^2+5^3+.....+5^{101}\)

\(\Rightarrow5A-A=\left(5^2+5^3+...+5^{101}\right)-\left(5+5^2+....+5^{100}\right)\)

\(\Rightarrow4A=5^{101}-5\)

\(\Rightarrow A=\frac{5^{101}-5}{4}\)