Question

30可以这样得到1+3=4×2=8+2=10×=30 证明 可以得到2∧100+2∧97-2

Answer 1

(1) 1 + 2 = 3,3*3 = 9,9*2 = 18,18 + 2 = 20,20 + 2 = 22.

(2) 2^100 + 2^97 - 2 = 2[2^96 - 1] + 2^100

= 2[1 + 2 + 2^2 + ...+ 2^95] + 2^100

= 2 + 2^2 + 2^3 + ...+ 2^96 + 2^100

1*2 = 2

2 + 2 + 2 = 2 + 2^2

2 + 2^2 + 2 + 2 + 2 + 2 = 2 + 2^2 + 2^3

...

2 + 2^2 + 2^3 + ...+ 2^95 + 2 + 2 + ...+ 2 [ 2^95 个 2相加]

= 2 + 2^2 + 2^3 + ...+ 2^95 + 2^96

2 + 2^2 + 2^3 + ...+ 2^96 + 2 + 2 + ...+ 2 [2^99 个2相加]

= 2 + 2^2 + 2^3 + ...+ 2^96 + 2^100