\(A=-1^2+2^2-3^2+4^2-...-99^2+100^2\)
\(=\left(2^2-1^2\right)+\left(4^2-3^2\right)+...+\left(100^2-99^2\right)\)
\(=\left(2+1\right)\left(2-1\right)+\left(4+3\right)\left(4-3\right)+...+\left(100+99\right)\left(100-99\right)\)
\(=1+2+3+4+...+99+100\)
\(=\frac{\left(1+100\right)\cdot100}{2}=5050\)
\(C=\left(2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}=\left(2^{64}-1\right)-2^{42}=-1\)
Mk chỉ bt làm câu C thôi tại vì mk chỉ học lớp 7
C=(2+1)(24+1)(28+1)(216+1)(232+1)-264
C=(24-1)(24+1)(28+1)(216+1)(232+1)-264
C=(28-1)(28+1)(216+1)(232+1)-264
C=(216-1)(216+1)(232+1)-264
C=(232-1)(232+1)-264
C=264-1-264
C=-1
