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$P_1$(person) can complete a job in $1^2$ day, $P_2$ can complete the same job in $2^2$ days. In general $P_n$ can complete the job in $n^2$ days. In how many days the job would be finished if an infinite number of distinct people do the job simultaneously?

My attempt:

Let the required number of days be $d$ then:

$$d=\large \frac{1}{\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...\frac{1}{n^2}...}=\frac{6}{\pi^2}$$

Am I right?

AhmedBajwa
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1 Answers1

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Your answer is correct. It may be that you are expected to explain that the combined rate is $1+\frac{1}{2^2}+\frac{1}{3^2}+\cdots$, and to give some sort of reference for Euler's closed form for $\zeta(2)$.

André Nicolas
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