![]() Shifting of exponents was explained in the previous lesson. As mentioned above, the same process for shifting the exponent is used for Step (4). In Step (b) above, we added and subtracted the same term, that term being the common ratio raised to the exponent 1. Our method for shifting the exponent in Steps (3) and (4) may cause some confusion for students. In the above solution, we started by changing the index of summation (students may want to, as an additional exercise, try to solve this problem by first changing the exponent). To convert our series into this form, we can start by changing either the exponent or the index of summation. Students should immediately recognize that the given infinite series is geometric with common ratio 2/3, and that it is not in the form to apply our summation formula, Possible Mistakes and Challenges Getting started
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