Prove the formula for the sum of the squares of the first n positive integers: n

Question:

Prove the formula for the sum of the squares of the first n positive integers:

n i = 1 + 2 + 3 + i=1 + n?. n(n + 1)(2n + 1) 6

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9780495011606

6th Edition

Authors: James Stewart

See More Books

Question Posted: Nov 09, 2023 12:03 PM

See More Questions

The signed-rank statistic can be represented as S + = 1 U 1 + 2 U 2 +.....+ n U n where U i = 1 if the sign of the (x i 0 ) with the ith largest absolute magnitude is positive (in which case i...
LAB 5.3 Working with the for loop Bring the for.cpp from the Lab 5 folder. This program has the user input a number n and then finds the mean of the first n positive integers. ?? The code is shown...
An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed...
Why might management analyze product profitability?
Make scatterplots for all pairwise combinations of the variables from the tree data (Table 1.7). Which pairs of variables have the strongest relationship? Is your conclusion consistent with prior...
A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the...
Lahey Corp. has three defined-benefit pension plans as follows. How will Lahey report these multiple plans in its financial statements? Plan X Plan Y Plan Z Pension Assets (at Fair Value) $600,000...
A car traveling 87.0 km/h is 1500 m behind a truck traveling at 74.0 km/h. How far from its initial position does the car have to travel to catch up to the truck.
Problem Statement: The aim of this case study is to propose a daily capacity level and level of resourcing required for Q2 & Q3 2023. The proposed daily capacity level should achieve the highest...
If cos = 2/5 and 0 < < /2, find the other five trigonometric functions of .
Sketch the region bounded by the parabola x = y 2 and the line y = x 2.
In Problem solve the matrix games using a geometric linear programming approach. 4 -2 3
Consider the following two companies (they operate in the same region with taxes equal to 30%): Company A: Sells goods for $3.1 per unit at costs of $1.9 to achieve a total revenue of $5,425 a year....
An investor researching profitable companies pulls quarterly reports of various corporations. The reports are prepared according to GAAP with objective information and focus on the business as a...
Delin started his first job at the age of 22. He was not able to start saving for retirement right away due to some constraints but started putting aside $7200 per year when he was 26. How much can...
a. Calculate Riverside's financial ratios for 2014. Assume that Riverside had $1,000,000 in lease payments and $1,400,000 in debt principal repayments in 2014. (Hint: Use the book discussion to...
Joleen is concerned whether an insurance company she found online is going to be in business when she retires in 20 years. What is something she can look at to evaluate the safety of the insurance...
Union Electric sold $5,000,000, 5%, 10-year bonds on January 1, 2014. The bonds were dated January 1 and pay interest on January 1. The bonds were sold at 103. Instructions (a) Prepare the journal...
How will relating product contribution margin s to the amount of the constrained resource they consume help a company maximize its profits?
In problem, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function...
In problem, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function...
In problem, match each graph to its function. A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function...
3. Consider the linear system 3x y + z = 2x+4y-z 3 = 5 -y+2z == 1 (a) Prove that the Jacobi method converges to the exact solution x = [111]. (b) Solve this linear system using MATLAB functions...
Consider the function f(x) 1 sin(x) (a) (3 points) Is f(x) well-conditioned or ill-conditioned for values of a close to ? Is f(x) well-conditioned or ill-conditioned for values of a close to 0.5? To...
Problem 1. Given the following list of numbers, [20, 0, 10, 6, 4, 9, 14, 15, 7, 13], answer the following questions: 1. How would the list look like after three complete passes of bubble sort? 2. How...

Prove the formula for the sum of the squares of the first n positive integers: n

Question:

n Σ i = 1 + 2 + 3 + i=1 + n?. n(n + 1)(2n + 1) 6

Step by Step Answer:

1 Let S be the desired sum We start with the telescoping sum or collapsing sum 2 Let S n ...View the full answer

Calculus

Students also viewed these Mathematics questions