a) \(M=2^2+2^4+.........+2^{100}\)
\(4M=2^4+2^6+........+2^{102}\)
\(4M-M=\left(2^4-2^4\right)+\left(2^6+2^6\right)+....+2^{102}-2^2\)
\(3M=2^{102}-2^2\)
\(M=\frac{2^{102}-4}{3}\)
b) \(M=2^2+2^4+..........+2^{100}\)
\(M=\left(2^2+2^4\right)+\left(2^6+2^8\right)+.........+\left(2^{98}+2^{100}\right)\)
\(M=\left(2^2.1+2^2.2^2\right)+\left(2^4.1+2^4.2^2\right)+.........+\left(2^{98}.1+2^{98}.2^2\right)\)
\(M=2^2.5+2^6.5+.............+2^{98}.5\)
\(M=5.\left(2^2+2^6+...........+2^{98}\right)\)
Vậy M chia hết cho 5 => (đpcm)
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