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1. Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer.
2. Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer.
3. Use mathematical induction to show that 3 divides n^3+2n whenever n is a nonnegative integer.
Prepare the equation of the rectangular hyperbola - Find the equation of the rectangular hyperbola
State the value of the discriminant and then describe the nature of the solution. What is the value of the discriminant?
There are six sections of Math with a total enrollment of one hundred and ninety nine students, what is the smallest possible number of students in the section with the largest enrollment?
Kurt Daniels wants to buy a $30,000 car. He has saved $27,000. Find the number of years it will take for his $27,000 to grow to $30,000 at 4% interest compound quarterly.
Find the p-value for each of the following hypothesis testing situations.
Description of Directional Derivative and how the dot product can be used to justify that the gradient points in the direction of maximum of a function.
Prepare the name of congruent angles from the given figure - Name every angle that is congruent to (has the same measure as) angle ACD.
Multiple choice question from Probability and Set Language and valid probability distribution for a sample space
Let H be a group and tau_1 : H ---->G_1, tau_2 : H ----> G_2, ... , tau_n : H -----> G_n homomorphism with this property: whenever G is a group and g_1 : G ---->G_1, g_2 : G ----G_2, ..., g_n : G ----> G_n are homomorphism
A cyclic group is a special kind of group that has many similarities with modular arithmetic.
Write an equation using the following information: Each represents an exponential function with base 2 or 3 translated and/or reflected
Flying with the jetstream, the same jet travels 4600km in 4 hours. What is the speed of the jet in still air, and what is the speed of the jetstream?
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