(1) (Telescoping series) This infinite series is convergent since we can break up each fraction and cancel almost all terms: 1:2 + 2.3 + 3.4- 1 + ... + 99.100 + . .. (2) For two non-negative series, if the bigger one is convergent, then the smaller one is also conver- gent. Solve the following problems. 1 1 1. Explain why the series 2 + 99 100 + ... is convergent with detail. 1 7 2. Explain why the series - 1 + 22 32 + 2 + ...+ 992 1002 + . . . is convergent with detail. 3. We now continue with the mouse-eating-cheese problem, Problem 3 of Wk6b. On the first day, the mouse will eat , of what is available. On the second day, it will eat , of the leftover from the previous day. On the kth day, , it will eat , of the leftover from the k - 1th day. Is there any cheese left after an infinitely many days