4+44+444+4444+44444+...n个4
=4*(1+11+111+1111+...n个1)
=4*(10^(n-1)+2*10^(n-2)+...+k*10^(n-k)+...+n)
n+11n+111n+1111n+......+1111111n
a(i) = 4*(10^i-1)/9
sum(a(i)) = 4/9* (sum(10^i) -i) = 4/9 * ( 10/9 * (10^i - 1) - i )
其中i取1,2,3...
原式=4×(1+11+111……1111111)
=4×1234567
=4938268