Question

平方差、、初一数学题

图片。。。

Answer 1

(1+1/2)(1+2^2)(1+1/2^4)(1+1/2^8).....(1+1/2^32)+2^-63
=(1+1/2)(1+2^2)(1+1/2^4)(1+1/2^8).....(1+1/2^32)+1/2^63
=2*(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8).....(1+1/2^32)+1/2^63
=2*(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8).....(1+1/2^32)+1/2^63
=2*(1-1/2^4)(1+1/2^4)(1+1/2^8).....(1+1/2^32)+1/2^63
=2*(1-1/2^8)(1+1/2^8).....(1+1/2^32)+1/2^63
=2*(1-1/2^16).....(1+1/2^32)+1/2^63
...........
=2*(1-1/2^32)(1+1/2^32)+1/2^63
=2*(1-1/2^64)+1/2^63
=2*-1/2^63+1/2^63
=2

(2^2+4^2+...+2^100)-(1^2+3^2++......+99^2)
=2^2+4^2+......+100^2-1^2-3^2-......-99^2
=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
=(1+100)*100/2
=101*50
=5050

Answer 2

1. (2+1)/2x(2^2+1)/2^2x(2^4+1)/2^4x(2^8+1)/2^8=[(2+1)(2^2+1)(2^4+1)(2^8+1)]/2^(1+2+4+8)
2. 1+1/2^32+2^-63=(2^32+1+2^-31)/2^32
3. (2^2+4^2+……+100^2)-(1^2+3^2+……+99^2)=y
[ y+(1^2+3^2+……+99^2)]x(1^2+3^2+……+99^2)
=y(……)+(……)^2
y=2^2-1^2+4^2-3^2+……+100^2-99^2
=1+2+3+4+……+99+100
=5050
sp: y^2-z^2=(y+z)(y-z)