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Pre-Calculus Tutoring in Carmel Arts & Design District, IN
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Recent Tutoring Session Reviews
When we had gone over the two basic types of series, I spent time showing her examples and asking her to find the patterns and thus define the series. Then I had her convert things into summation notation. Finally, we ended on working through some more challenging series problems concerning non-standard series.
Overall, she seemed to struggle a little bit with expressing a pattern she could identify in the series as a general rule using the index (n). The last few problems we went over seemed to help her get a better grasp on it though, and I left her with a recommendation that she practice problems that ask her to express the general a_n term given a series."
We then discussed how to use the summation formulas. We calculated both partial and infinite sums. We used the explicit formulas to find the necessary information to calculate the sums in problems where the given information wasn't sufficient. We focused particularly on infinite sums and highlighted the series we could and could not calculate a convergent sum.
Another topic on which we focused was the conversion of series to sigma notation and back. We discussed what the numbers below and above the sigma meant and for what they were used. We covered how sigma notation would differ when expressing a partial sum to when expressing an infinite one.
She didn't have too much difficulty with the topics except for formulating sequences/series for a situation described by a word problem. So we learned a method of "pattern finding" where we would list the un-evaluated expressions for the terms of a sequence/series to try and discern a pattern. After recognition, we could then write an explicit formula for the sequence with which we used to solve the given word problem."