A=(2+22) +(23+24)+......+(259+260) = 2(1+2) +23(1+2) + ......+ 259(1+2) = 3(2+23+ 25+......+ 259) chia hết cho 3
A=(2+22+23)+(24+25+26) + ...........+(258+259+260)= 2 (1+2+22) +24 (1+2+22) +.................+ 258 (1+2+22)
= 3.7 + 24.7 +................+ 258.7 chia hết cho 7
A= (2+23) + ( 22+ 24) +(25+27) +(26+28) +...................+ (258+260)
=2(1+22) +22 (1+22) +25 (1+22)+26(1+22) + ..................+ 258 (1+22) = 2. 5 + 22 .5 +.............+258.5 chia hết cho 5
mà A chía hết cho 3 => A chia hết cho 3.5 =15
\(A=2+2^2+2^3+2^4+2^5+...+2^{60}\)
\(\Rightarrow2A=2.\left(2+2^2+2^3+2^4+2^5+...+2^{60}\right)\)
\(2A=2^2+2^3+2^4+2^5+2^6+...+2^{61}\)
Vậy \(2A-A=\left(2^2+2^3+2^4+2^5+2^6...+2^{61}\right)-\left(2+2^2+2^3+2^4+2^5+...+2^{60}\right)\)
\(A=2^{61}-2\)
