Question

Tính:

A= -1^2+2^3-3^2+4^2....-99^2+100^2

B=(2+1).(2^4+1).(2^8+1).(2^16+1)

Answer 1

câu a sai đề

b. Ta có : B = (2+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

⇒ 3B = 3(2-1)(2+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

= (2²-1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

= (2⁴-1)(2⁴+1)(2⁸+1)(2¹⁶+1)

= (2⁸-1)(2⁸+1)(2¹⁶+1)

= (2¹⁶-1)(2¹⁶+1)

= 2³²-1

⇒ B = \(\dfrac{2^{32}-1}{3}\)

Answer 2

\(A=2^2-1^2+4^2-3^2+...+100^2-99^2\)

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

=1+2+3+4+...+99+100

=5050