You probably have seen the formula E1 i= 5n² +5n This means that if you want to know the sum of the first 100 natural number, this number is 1+2+3+ ...+ 100 = 1002 +100 t is told that this formula was proven by Gauss at the age of 5, when the kindergarten teacher gave er students this problem, tired of the noise that they were making. Turns out, there are infinitely nany of these formulas. If you want to know the value of the sum of the first n numbers raised to the =-th power Ei* = ao +a1n+.+ ak+1nk+1 i=1 For example: 1 1 E =1+2° + 3² + -..+n² = =n° + zn² + 6' i=1 Notice that when you want to sum the squares of numbers, the formula will yield a polynomial of legree 3 and more in general if you sum the kth power of numbers you will get a polynomial of degree =+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 Matlah and give the formula
You probably have seen the formula E1 i= 5n² +5n This means that if you want to know the sum of the first 100 natural number, this number is 1+2+3+ ...+ 100 = 1002 +100 t is told that this formula was proven by Gauss at the age of 5, when the kindergarten teacher gave er students this problem, tired of the noise that they were making. Turns out, there are infinitely nany of these formulas. If you want to know the value of the sum of the first n numbers raised to the =-th power Ei* = ao +a1n+.+ ak+1nk+1 i=1 For example: 1 1 E =1+2° + 3² + -..+n² = =n° + zn² + 6' i=1 Notice that when you want to sum the squares of numbers, the formula will yield a polynomial of legree 3 and more in general if you sum the kth power of numbers you will get a polynomial of degree =+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 Matlah 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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PLEASE answer question NUMBER 4 only, please be clear and thanks in advance for answering only number 4.
Transcribed Image Text:You probably have seen the formula E- i = }n² + }n This means that if you want to know the sum
of the first 100 natural number, this number is
1
+-100
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
¿* = ao + a¡n + . .+ ak+1nk+1
ik
For example:
1
1
E² = 1+22 + 32 + · . + n² =
+교 + 공
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.
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