A = 1 + 2 + 22 + 23 + ..... + 2100
=>2A=2+22+23+...+2101
=>2A-A=2+22+23+...+2101-(1 + 2 + 22 + 23 + ..... + 2100)
A=2+22+23+...+2101-1-2-22-23-...-2100
=2101-1
=>A=B=2101-1
\(A=1+2+2^2+2^3+.....+2^{100}\)
\(2A=2+2^2+2^3+2^4+.....+2^{101}\)
\(2A-A=2+2^2+2^3+2^4+.....+2^{101}-\left(1+2+2^2+2^3+.....+2^{100}\right)\)
\(A=2+2^2+2^3+2^4+.....+2^{101}-1-2-2^2-2^3-....-2^{100}\)
\(\Rightarrow A=2^{101}-1\)
\(\Rightarrow A=B\)
chúc bạn học giỏi^^