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Long-Term Actuarial Math Old Exam MLC Forum

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Old 08-13-2018, 07:33 PM
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Default Textbook exercise 2.1g

Maybe I'm missing something here, but the solution manual calculates ∑ (1 - x/55)^(1/5) from 1 to 54 as 45.18 without any steps. My handy dandy Wolfram Alpha gives the correct answer though no steps... Is this something that should easy to compute by hand?
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Old 08-13-2018, 10:17 PM
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There's no analytical formula for the sum. It is monotonic decreasing so the value would be greater than the integral from 1 to 55 and less than the integral from 0 to 54. You would probably get a good approximation by averaging the two integrals.
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Old 08-15-2018, 03:23 PM
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There's no analytical formula for the sum. It is monotonic decreasing so the value would be greater than the integral from 1 to 55 and less than the integral from 0 to 54. You would probably get a good approximation by averaging the two integrals.
Thanks for the reply. Definitely did not think of using an approximation like this... Evidence of my rusty math skills lol
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Old 08-15-2018, 04:55 PM
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Thanks for the reply. Definitely did not think of using an approximation like this... Evidence of my rusty math skills lol
Computing the sum with Excel gives 45.1767514..., which rounds to the textbook's 45.18. The suggested approximation gives 45.1473... , which is only off by 0.065%---not bad!
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