You probably have seen the formula , i = ;n2 + n This means that if you want to know the sum of the first 100 natural number, this number is 1002 +100 2 1+2+3+...+ 100 = It is told that this formula was proven by Gauss at the age of 5, when the kindergarten teacher gave her students this problem, tired of the noise that they were making. Turns out, there are infinitely many of these formulas. If you want to know the value of the sum of the first n numbers raised to the k-th power (*)> i* = ao + a1n + · · · + ak+1nk+1 i=1 For example: n E² = 1+22 + 3² + ... + n² = 1 + 2 1 + zn 3 6' i=1 Notice that when you want to sum the squares of numbers, the formula will yield a polynomial of degree 3 and more in general if you sum the kth power of numbers you will get a polynomial of degree k +1. The goal is to find the formula for k = 6. 1. Specialize the formula in (*) for k = 6. 2. What are the variable you want to solve for? 3. How many equations do you need? 4. Find a system of 8 different equations. 5. Solve the system with Matlab and give the formula.

You probably have seen the formula , i = ;n2 + n This means that if you want to know the sum of the first 100 natural number, this number is 1002 +100 2 1+2+3+...+ 100 = It is told that this formula was proven by Gauss at the age of 5, when the kindergarten teacher gave her students this problem, tired of the noise that they were making. Turns out, there are infinitely many of these formulas. If you want to know the value of the sum of the first n numbers raised to the k-th power ()> i = ao + a1n + · · · + ak+1nk+1 i=1 For example: n E² = 1+22 + 3² + ... + n² = 1 + 2 1 + zn 3 6' i=1 Notice that when you want to sum the squares of numbers, the formula will yield a polynomial of degree 3 and more in general if you sum the kth power of numbers you will get a polynomial of degree k +1. The goal is to find the formula for k = 6. 1. Specialize the formula in (*) for k = 6. 2. What are the variable you want to solve for? 3. How many equations do you need? 4. Find a system of 8 different equations. 5. Solve the system with Matlab and give the formula.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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