(999 8 / 9 + 1 / 9) + (999 8 / 9 + 1 / 9) + (999 8 / 9 + 1 / 9)

(999 8 / 9 + 1 / 9) + (999 8 / 9 + 1 / 9) + (999 8 / 9 + 1 / 9)

(999 8 / 9 + 1 / 9) + (999 8 / 9 + 1 / 9) + (999 8 / 9 + 1 / 9)
=999+8/9+1/9+99+8/9+1/9+9+8/9+1/9
=999+1+99+1+9+1
=1110

(1+100+100^2+100^3+…… +100^99)/(1+2+3+…… +98+99+100+99+98+…… +2+1）^50-1
Explain why

(1+100+100^2+100^3+…… +100^99)/(1+2+3+…… +98+99+100+99+98+…… +2+1）^50-1
=[(100^100-1)/99] / [(100*100)^50-1]
=(100^100-1)/99*1/(100^100-1)
=1/99

Calculate 1 * 3 + 3 * 3 ^ 2 + 5 * 3 ^ 3 +. + 99 * 3 ^ 50

Using the dislocation subtraction method, Sn = 1 * 3 + 3 * 3 ^ 2 + 5 * 3 ^ 3 + 7 * 3 ^ 4 + +(2n-1) * 3 ^ n multiply this equation by 3 to get: 3Sn = 1 * 3 ^ 2 + 3 * 3 ^ 3 + 5 * 3 ^ 4 + 7 * 3 ^ 5 + +(2n-3) * 3 ^ n + (2n-1) * 3 ^ (n + 1) the first formula minus the second formula, we get - 2Sn = 3 + 2 (3 ^ 2 + 3 ^ 3 + 3 ^ 4 +...) ...