Question

计算： (1+29)(1+ 29 2 )(1+ 29 3 )…(1+ 29 30 )(1+ 29 31 )

计算： (1+29)(1+ 29 2 )(1+ 29 3 )…(1+ 29 30 )(1+ 29 31 ) (1+31)(1+ 31 2 )(1+ 31 3 )…(1+ 31 28 )(1+ 31 29 ) =______．

Answer 1

(1+29)(1+ 29 2 )(1+ 29 3 )…(1+ 29 30 )(1+ 29 31 ) (1+31)(1+ 31 2 )(1+ 31 3 )…(1+ 31 28 )(1+ 31 29 ) = 30 1 × 31 2 × 32 3 ×…× 59 30 × 60 31 32 1 × 33 2 × 34 3 ×…× 59 28 × 60 29 = 30×31×32×…×59×60 1×2×3×…×30×31 32×33×34×…×59×60 1×2×3×…×28×29 = 30×31×32×…×59×60 1×2×3×…×30×31 × 1×2×3×…×28×29 32×33×34×…×59×60 =1 故填：1．