Question

Find a formula for the sum of the squares of the numbers 1, 2, ...., n and prove it by induction.

Answer #1

The product of two numbers is 1 and the sum of their squares is
2. Find the numbers.

Find the sum of squares 1^2 + 2^2 + ... n^2 using iteration and
recursion
* I'm guessing we need to modify it
Here's the code unmodified
public class Sum {
//Non recursive sum
public static long sum1 (int n) {
long sum = 1L;
for (int i = 2; i <= n; ++i)
sum = sum + i *i ;
return sum;
}
//Recursive sum
public static long sum2 (int n) {
if (n < 2)return 1L;
return sum2(n...

Find all natural numbers n so that
n3 + (n + 1)3 > (n +
2)3.
Prove your result using induction.

Find three numbers whose sum is
3333
and whose sum of squares is a minimum.

Find three positive numbers whose sum is 12, and whose sum of
squares is as small as possible, (a) using Lagrange multipliers
b)using critical numbers and the second derivative test.

1) Explain the
Regression Sum of Squares (RSS)
2) Explain the
Residual Sum of Squares (RSS)
3) What is the formula
for calculating Mean Squares?
Regression Output - 2
ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
3722496657566
1
3722496657566.014
4132
.000b
Residual
2196018240410
2438
900745791.801
Total
5918514897976
2439
a. Dependent Variable: Sale Price
b. Predictors: (Constant), Appraised
Land Value

Given 2 4-sided dice (1,2,4,6)
1)Find the total numbers of outcomes
2)Find the sum of the outcomes
3)Find the distribution of the Sum of the outcomes
4)Find the average of the sum of outcomes.
Is this probability distribution? Why or why not? Is yes then
graph using a histogram to prove it.

Prove by induction on n that 13 | 2^4n+2 + 3^n+2 for all natural
numbers n.

Three numbers x, y, and z that sum to 99 and also have their
squares sum to 99. By Lagrange method, find x, y, and z so that
their product is a minimum.

The sum of squares and the products of every pair of n
non-negative real numbers X1, . .., Xn are known, however X1, ... ,
Xn are not known. Based on this information
(A) both the mean and the standard deviation of these numbers
can be determined.
(B) neither the mean nor the standard deviation of these numbers
can be determined.
(C) the mean can not be determined but the standard deviation of
these numbers can be determined.
(D) the...

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