# Question:"The Basel problem "in Student Basics

## Question:"The Basel problem "in Student Basics

Maple 2024

I just discoverd today the step solutions for series in Student package

Now i try to solve this with my own steps here ..

Note: was not capable to get a closed form?

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Euler's Basel Problem
In the Student Basics package, there is a command :

generate steps for evaluating summations

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The SummationSteps command accepts an expression that is expected to contain summations and displays the steps required to evaluate each summation given.

with(Student[Basics])

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Try this out this command for the Basel problem series  ( p-series example)

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Now the Basel Problem from Euler

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How do we get this value from Euler ( The Basel Problem)

 > # Step 1: Define the series f f := sum(1/n^2, n = 1 .. infinity); # Step 2: Write the series as a product of terms (1 - 1/p) g := convert(product(1 - 1/p, p = primes), hypergeom); # Step 3: Compare with the Taylor series of the sine function h := series(sin(x), x = 0, 10); # Step 4: Set up equations between corresponding terms eq := seq(coeff(h, x, 2*k)/k!, k = 1 .. 5) =       seq(coeff(g, x, k), k = 1 .. 5); # Step 5: Solve the equations to find the value of the series sol := solve({eq, seq(coeff(g, x, k) = 0, k = 6 .. 10)}); # Step 6: Replace x with pi/2 to find the value sol_pi := subs(x = Pi/2, sol); # Step 7: Compute the value of the series value := sol_pi[1][2]; value;
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