Question

初一数学题、

见图片、、

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+1/2）（1+1/2^2)(1+1/2^4)....(1+1/2^32)+2^(-63)
=2*(1-1/2)（1+1/2）（1+1/2^2)(1+1/2^4)....(1+1/2^32)+2^(-63)
=2(1-1/2^2)(1+1/2^2)(1+1/2^4)....(1+1/2^32)+2^(-63)
=........=2(1-1/2^64)+1/2^63
=2
(2^2+4^2+6^2+...+100^2)-(1^2+3^2+5^2+....+99^2)
=(2^2-1^2)+(4^2-3^2)+(6^2-5^2)+......+(100^2-99^2)
1+2+3+4+5+6+.....+99+10
=5050