Question

Bài 1: Tính:

a)A=3(2^2 + 1) (2^4 + 1) (2^16 + 1)

b)B=-1^2 +2^3 - 3^2 +4^2 -...- 99^2 + 100^2

c) C=-1^2 + 2^2 - 3^2 +4^2 - ... +(-1)^n (n ϵ N^*)

Answer 1

a: Sửa đề:  \(A=3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=2^{32}-1\)

b: \(B=-1^2+2^2-3^2+4^2-...-99^2+100^2\)

\(=\left(2-1\right)\left(2+1\right)+\left(4-3\right)\left(4+3\right)+...+\left(100-99\right)\left(100+99\right)\)

\(=1+2+3+...+99+100\)

=5050