Đặt B = 4^1993 + 4^1992 + ... + 4^2 + 4 + 1
=> 4B = 4^1994 + 4^1993 + ... + 4^3 + 4^2 + 4
=> 3B = 4^1994 - 1
Ta lại có:
A = 75B + 25 = 25.(3B+1) = 25.(4^1994 - 1 + 1) = 25.4^1994
Đặt \(B=4^{1993}+4^{1992}+...+4^2+5\)
\(B=4^{1993}+4^{1992}+...+4^2+4+1\)
\(\Rightarrow B=1+4^2+...+4^{1992}+4^{1993}\)
\(\Rightarrow4B=4+4^3+...+4^{1993}+4^{1994}\)
\(\Rightarrow4B-B=\left(4+4^3+...+4^{1993}+4^{1994}\right)-\left(1+4^2+...+4^{1992}+4^{1993}\right)\)
\(\Rightarrow3B=\left(4^{1994}+4-1\right)\)
\(\Rightarrow3B=4^{1994}+3\)
\(\Rightarrow B=\left(4^{1994}+3\right):3\)
\(\Rightarrow A=75.\left(4^{1994}+3\right):3+25\)
\(\Rightarrow A=25.\left(4^{1994}+3\right)+25\)
\(\Rightarrow A=25.\left(4^{1994}+3+1\right)\)
\(\Rightarrow A=25.\left(4^{1994}+4\right)\)
\(\Rightarrow A=4^{1994}.25+100\)
Vậy \(A=4^{1994}.25+100\)
