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Section 10.3 5. Rewrite each geometric series using the sigma notation and calculate the value of the sum. 1 1+ - 6. The mathematical diet you are following says you can eat "half of whatever is on the plate," so first you bite off one half of the cake and put the other half back on the plate. Then you pick up the remaining half from the plate (it's "on the plate"), bite off half of that, and return the rest to the plate. And you continue this silly process of picking up the piece from the plate, biting off half, and returning the rest to the plate. (a) Represent the total amount you eat as a series. (b) How much of the cake is left after 1 bite, 2 bites, n bites? (c) "Eventually," how much of the cake do you eat? Section 10.4 7. Show that the function determined by the terms of the given series satisfies the hypotheses of the Integral Test, and then use the Integral Test to determine whether the series converges or diverges. 1 (2k + 1)5