(1) How to divide $100 among four people according to given proportions: 1 : 2 : 4 : 8? (Use fractions only) (2) How to divide $100 among four people according according to given proportions: 1: ? : ? : : ? (Use fractions only) 2. (1) What is the value of the sum 1+ 2+4+ 8+ . ..+ 2"-1, where n is any positive integer? (2) What is the value of the sum It ? tit tit mn-1, where n is any positive integer? (3) Justify that 1 + 7 + 3 + 4 Itt. + + ... =0. (The sum is unbounded.) 3. (1) What is the value of the sum + ; 1 + 12 1 + 20 +... + 1 6 99 .100 NIH NIL (2) What is the value of the sum + 1 12 20 + ... +; n(n+1), where n is an positive integer? (3) What is the value of the infinite sum tot 12 + 20 + . .. + (n+ 1 ) +