\(S=1+2^2+2^4+2^6+2^8+...+2^{2024}\\2^2\cdot S=2^2\cdot(1+2^2+2^4+2^6+2^8+...+2^{2024})\\4S=2^2+2^4+2^6+2^8+2^{10}+...+2^{2026}\\4S-S=(2^2+2^4+2^6+2^8+2^{10}+...+2^{2026})-(1+2^2+2^4+2^6+2^8+...+2^{2024})\\3S=2^{2026}-1\\\Rightarrow S=\dfrac{2^{2026}-1}{3}\\Toru\)