Complete the proof of theorem 2. 4. 6 by showing that if the series [infinity] n=0 2nb2n diverges, then so does [infinity] n=1 bn. Example 2. 4. 5 may be a useful reference.

What is the pattern in the values as the exponents increase?

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Aschool allots ? 1500 to spend on a trip to the theatre. theatre tickets have a regular cost of ? 55 each and are on offer for 1 5 off. a train ticket for the day will cost ? 12 each. if 2 teachers and the maximum number of students attend, how much money will the school have left over?