I really need help with this question. It would mean a lot if someone can help. Please answer part 4 of this question. Thank you so much! I am struggling with both parts 4 and 5 but please at least question 4 is enought. Thanks! You probably have seen the formula E1 i = ;n2 + n This means that if you want to know the sumof the first 100 natural number, this number is2=11+2+3+..+ 100 =1002 +100It is told that this formula was proven by Gauss at the age of 5, when the kindergarten teacher gaveher students this problem, tired of the noise that they were making. Turns out, there are infinitelymany of these formulas. If you want to know the value of the sum of the first n numbers raised to thek-th power(*) E ik= ao + a1n +·.+ ak+1n*+1i=1For example:E2 =1+ 22 + 3² ++n?:13112n² + zn6"i=1Notice that when you want to sum the squares of numbers, the formula will yield a polynomial ofdegree 3 and more in general if you sum the kth power of numbers you will get a polynomial of degreek +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 doyouneed?4. Find a system of 8 different equations.5. Solve the system with Matlab and give the formula.

Please check step 2 for the solution.

You probably have seen the formula E, i = }n² + ;n This means that if you want to know the sur of the first 100 natural number, this number is 1 1002 +100 2 1 1+2+3+...+ 100 = It is told that this formula was proven by Gauss at the age of 5, when the kindergarten teacher gav her students this problem, tired of the noise that they were making. Turns out, there are infinitel many of these formulas. If you want to know the value of the sum of the first n numbers raised to th k-th power k+1 = ao + ajn +···+ ak+1n i=1 For example: n 1 1 nº + 2 1 2 E? = 1+ 22 + 32 + +n? 6" .. i=1 Notice that when you want to sum the squares of numbers, the formula will yield a polynomial degree 3 and more in general if you sum the kth power of numbers you will get a polynomial of degre 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.

You probably have seen the formula E, i = }n² + ;n This means that if you want to know the sur of the first 100 natural number, this number is 1 1002 +100 2 1 1+2+3+...+ 100 = It is told that this formula was proven by Gauss at the age of 5, when the kindergarten teacher gav her students this problem, tired of the noise that they were making. Turns out, there are infinitel many of these formulas. If you want to know the value of the sum of the first n numbers raised to th k-th power k+1 = ao + ajn +···+ ak+1n i=1 For example: n 1 1 nº + 2 1 2 E? = 1+ 22 + 32 + +n? 6" .. i=1 Notice that when you want to sum the squares of numbers, the formula will yield a polynomial degree 3 and more in general if you sum the kth power of numbers you will get a polynomial of degre 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.

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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