For every positive integer n     12+22+32+...+n2=n(n+1)(2n+1)/6 Let S(n)=12+22+32+...+n2 How do you get the basic and inductive step

Q: Why k(k+1) is an even number?

A: We have to tell just  that why k(k+1) is an even number.Here we considering that you understood  the…

Q: For Exercise, evaluate the expression. (n – 1)! (n + 1)!

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Q: the statement below true or false for n=1? ©George Mason University 2+ 4 + 6+ ... + 2n = n² + n + 1

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Q: So an = n 16 n+ 16 (n-1) 16 (n-1) + 16 = n - 16 n+ 16 I X 11 (n + 15) (n + 16)

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Q: With induction, prove that 1*2 to the power of 0 + 2*2 to the power of 1 + 3* 2 to the power of 2 +…

A: To prove

Q: Q1 (b): If Xi= 1,3,5,7,9,11 and Yi= 0,2,4,6,8,10. The values of the :following term is i=n 2n – 3…

A: Given,∑i=1i=n2n-3πyi-11+xii-1here n=6

Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: ) 6. Express the sum 9 + 28 + 65 + ... + (n'+1) using E-notation.

A: We have to find sum of series:

Q: Using induction, verify that 12 + 32 + 52 + ... + (2n -1)2 = n(2n -1)(2n +1) / 3 is true for every…

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Q: Q5. Describe the principle of mathematical induction and prove P(n) =1 + 2 + 22 +..+ 2" = 2n+1 - 1…

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Q: Determine the correct expression for L{6u(t+2)+&e4t – 58(t) Oa. 5 8-4 O b. be-2 - 5e- 8-4 6e2s - 5e-…

A:

Q: Malik currently has 39 tulips in his yard. Each year he plants 3 more. (a) Which of the following is…

A: given data  malik havs 39 tulips in his yard each year he plants 3 more  so,  p0= 39 d = 3

Q: For each positive integer n, let P(n) be the property 5n − 1 is divisible by 4. Write P(0). Is P(0)…

A: Principles of mathematical induction : Algorithm: Obtained P(n) and understand it's meaning.  Prove…

Q: Simplification of the boolean expression (A+B+C)(D+E)'+(A+B+C)(D+E) yields which results

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Q: >(6k – 4)(7k + 3) - k=1 Enter your answer as a number without any arithmetic symbols. Sum =

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Q: (b) Show that 1 11 2 k(k + 2)(k + 4) 96 k=1

A: Given series is ∑k=1∞1kk+2k+4

Q: Serrm f the Senes

A: ∑n=1∞1 / (n+4) (n+5) = 1/5*6 + 1/6*7+... =1/5 =0.2

Q: 8(k+1)-4 8(n+1)-4 4 8k-4 is term to both sides of the equation. 4+12+20++ (8k-4)= 4k² +20++ (8k-4)+…

A: Topic:- application of algebra

Q: Use induction to prove that the sum of {n=-2} and {N} (4n − 5) = (n + 3)(2n − 9).

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Q: For each natural aumber a, the sum 1(2) + 2(3) ++ R(n + 1) is equal ta None of the choices This…

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Q: For each integer n2 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 72 - 6…

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Q: (Vn)(n2 +n+ 17 is prime)

A: Since, you have posted multiple questions , I am doing the very question (ques 7)  according to our…

Q: um 1+4+7+..

A:

Q: Use mathematical induction to show that n > 2n +1 for all integers n > 2.

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Q: (b) 6 + 7 + 8 + 9 + ... + k

A: (b) Given that 6+7+8+9+...+k The objective is to find the sum. The formula for sum of numbers are,…

Q: Oscar currently has 43 tulips in his yard. Each year he plants 8 more. (a) Which of the following is…

A: A recursive and explicit formula A recursive formula gives the worth of a particular term that…

Q: (Proof) For any integer n, n² + n is even.

A: We know the product of consecutive integers in a even integer.

Q: L(3tcos2t) is equal to? Select the correct response: O [3(s? + 4)]/(s? - 4) O (3s2 - 12)/(s² + 4)² O…

A: Laplace transferom of the function

Q: 2(n-3)+n(2-n)=2-n2

A:

Q: Simplify the following expressions by rewriting without any factorials. A. (n+1)! (n - 1)! (2n+1)!…

A: A)n2+n B)4n2+10n+61​ C) 4n2+2nExplanation:

Q: 7+ [9 x (7÷1)]

A: 7+ [9 x (7÷1)]

Q: Evaluate. (a) - 73 (b) ( – 7)3

A: Given query is to find the value of the expression.

Q: -n 2n+5

A: We have given a series.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.