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LongTerm Actuarial Math Old Exam MLC Forum 

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#1




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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#2




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.

#3




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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#4




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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Jim Daniel Jim Daniel's Actuarial Seminars www.actuarialseminars.com jimdaniel@actuarialseminars.com 
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