Prove the following. 1. The sum of four consecutive integers is even.

Q: 2. Find the Sum of the following terms -36, -28,-20,-12,...236

A:

Q: 100 How many solutions to the equation E Xx=3 k =1 have the property that each summand X, is a…

A: Number of solutions: The number of non-negative integer solutions to the equation are . Given:

Q: 5. Find the sum. 3A + 2B [1 -2 A = |0 -1 -1 2 1 2 and B = -3 2 [4 3 -61 -41

A: Here is the solution

Q: 1. Find a formula for the sum: 2+ 6+ 10 ... + 2(2n - 1)

A: The given sequence is 2+6+10+... +2(2n–1).

Q: Find the sum of n terms of an AP whose nth term is given by an=5-6n

A:

Q: 2+5+8+11+...293

A:

Q: Using the result you proved in the question above, find a list of 200 consecutive composite…

A:

Q: Solve this question, use pencil and paper to solve it, show your work as well.  1.  How many pairs…

A: How many pairs of two distinct integers chosen from the set  have a sum that is even ?

Q: Consider sum 1+5+9+13+...+81 what is a6

A:

Q: For how many values of n is the sum 1 + 2 + · • + n not divisible by n if 1 ≤ n < 100?

A:

Q: Find the sum 80 Σ 5n = n=11

A:

Q: Suppose I choose two numbers from the set {1, 2, 3,... 100}. How many have an even sum? Show all…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Solve for n. k (3-n) %3D

A: b=k(3-n)pbp=k(3-n)

Q: In how many ways can they line up so that no two geese are standing next to one another? (There is…

A: There are 10 ducks and 6 geese.

Q: 1 16. Sum 64+16+4+...+ 64

A:

Q: This is a mathematics question. There are 8 numbers in a sequence that add up to 250 (ex.…

A: The details are given as step 2.

Q: Find the smallest five consecutive composite integers.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A casino game consists of selecting two balls, without replacement, from an urn containing 7 balls…

A:

Q: Question 14, 6.2.53 University Law School accepts 1 out of every 7 applicants. If the school…

A: Let's find how many Students accepted.

Q: 2. What are the two largest positive integers n satisfying n - 1 | n²-A?

A:

Q: Q: The sum of the third and seventh terms of an A.P.is 6 and their product is 8. Find the sum of…

A: We know that  nth term of A.P is (an)=a+(n-1)d And sum of the terms (Sn)=n/2(2a+(n-1)d)

Q: Determine the sum in (국)". 2n=4

A:

Q: For how many n = {1, 2,…, 645} is n a multiple of one or more of 8, 7, or 3?

A: n belongs to (1,2,....645) is n a multiple of one or more of 8,7 or 3.

Q: um 1+4+7+..

A:

Q: Use permutations to solve. From a cooler with 9 different kinds of soda, 3 are selected for 3…

A: The formula of permutation is: Prn=n!n-r! This is the required answer.

Q: Prove that when you select n +1 numbers from {1,2, ... 2n} two of them must be consecutive (that is,…

A: Use inductive argument and Pigeon hole principles

Q: Express the sum in terms of n.

A: Given: ∑k=1nk2+3k+5

Q: If given a sequence of five consecutive integers (e.g. 1,2,3,4,5), then the sum of these integers is…

A:

Q: The sum of two integers with diff fit this description. 10

A: Given : To determine the two integers that will fit the condition            +          = -10

Q: The integers -10, -8, -6, -4, -2, 0, +2, +4, +6, and +8 LEARN ON ME.: are assigned to the letters W,…

A: Given: The integers -10, -8, -6, -4, -2, 0, +2, +4, +6, +8 are assigned to the letters W, L, E, O,…

Q: Without computing each sum, find which is greater, O or E, and by how much. O 5+7+9+11+...+101 E = 4…

A: