Question

Tìm 2 chữ sô tận cùng của \(2+2^2+2^3+...+2^{99}\) 

1 tỷ tik nha !!!!!!!

Answer 1

Put \(A=2+2^2+2^3+...+2^{99}\)

Infer \(2A=2^2+2^3+2^4+...+2^{100}\)

\(\Rightarrow2A-A=2^2+2^3+2^4+...+2^{100}-2-2^2-2^3-...-2^{99}\)

\(\Rightarrow A=2^{100}-2\)

Easy to see \(2^{100}=2^{4.25}\)Excess cessation takes the form \(2^{4n}\)

So \(2^{100}\)has the end number as 6

Candlesk \(2^{100}-2\)has the end number as 4

So \(2+2^2+2^3+...+2^{99}\)has the end number as 4