152+4752×51+47×4652×51×50+47×46×4552×51×50×49+…+47×46×45…×2×152×51×50×49…×6×5．

Question

(1)/(52)+(47)/(52×51)+(47×46)/(52×51×50)+(47×46×45)/(52×51×50×49)+…+(47×46×45…×2×1)/(52×51×50×49…×6×5)．

Answer 1

(1)/(52)+(47)/(52×51)+(47×46)/(52×51×50)+(47×46×45)/(52×51×50×49)+…+(47×46×45…×2×1)/(52×51×50×49…×6×5)
=(51504948+505494847+…+4321)/(4849505152)
=((1)/(5)×4849505152)/(4849505152)
=(1)/(5)