1+1-1+1-2+3-5+5-2+6-3+9+1-2+5-8+4+9-5+2+3-4+123-25+63+25-42+42-12+59-1+1008=?

1+1-1+1-2+3-5+5-2+6-3+9+1-2+5-8+4+9-5+2+3-4+123-25+63+25-42+42-12+59-1+1008=?

one thousand two hundred and forty

Find 1 + 11 + 111 + +111…… The general formula of 1

1+11+111+1111+111...1
=1+(10+1)+(10^2+10+1)+(10^3+10^2+1)+...+[10^n+10^(n-1)+...1]
=1×n+10(n-1)+10^2(n-2)+...+10^n[n-(n-1)]
Let Sn = 1 × n + 10 (n-1) + 10 ^ 2 (n-2) +... + 10 ^ n (1)
10sn=10+10^2(n-1)+10^3(n-2)+...+10^(n+1)n(2)
∴(1)-(2):
-9Sn=n+[10+10^2+10^3+10^n]-10^(n+1)n
-9Sn=n-10^(n+1)+{10[1-10^n]/(1-10)}
={n-10^(n+1)}-{10[1-10^n]/9}
∴Sn={-{n-10^(n+1)}/9}-{10[1-10^n]/81}
=10^(n+1)/9-(n/9)-{10[1-10^n]/81}

1-111 = 11 move a match to make the formula true

1-1+1=1