2^50-2^49-2^48-2^47-2^46-2^45-2^44-2^43-2^42-2^41-2^40-2^39-
1个回答

设S=-2^49-2^48-2^47-2^46-2^45-2^44-2^43-2^42-2^41-2^40-2^39-···-2^2-2-1 式(1)

2S=-2^50-2^49-2^48-2^47-2^46-2^45-2^44-2^43-2^42-2^41-2^40-2^39-···-2^2-2 式(2)

式(2)-式(1)得

S=-2^50+1

所以2^50-2^49-2^48-2^47-2^46-2^45-2^44-2^43-2^42-2^41-2^40-2^39-···-2^2-2-1=2^50+S=2^50-2^50+1=1