2 Look at the following picture. 000 000 1st term 2nd term 3rd term Prove that the number of matchsticks can be formulated as Un = n² + 3n + 2.

Q: 10 +(-1)" · n How many terms are needed to estimate to 5n n=0 within 0.1? Justify your answer!

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Q: The coefficients of three consecutive terms in the expansion of (1 + ay" are in the ratiol: 7:42.…

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Q: If a_1=10a1​=10 and a_n=a_{n-1}+1an​=an−1​+1 then find the value of a_4a4

A: Explanation of the answer is as follows

Q: 9. Prove the formula n(n+1) >i =1+2+...+n= 2 i=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: ( a ) Ση-1 (b) En=2 n7-1 15n-2 (c) En=1 11n+3 1 (d) Σn1 n14 (-1)" (e) En=1 7n+4

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Q: Find the radius of convergence and interval of convergence of  Σ 2 to infinity ((x+2)^n)/(2^n)(ln n)

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Q: i. Find the smallest integer K larger or equal to 1+ V53 + 46

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Q: 26 E(- 1)"2n - %3D n=0

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Q: A vial of radioactive material is found at a site where it was left unattended. At the time the vial…

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Q: 2) S(n)-10-2 at n 5

A: Given ,  f(n) = 10 (2)n     ......... (1) We have to find the value at n = 5 Put ,  n = 5 in…

Q: 19. According to Table B, P (z < -1.7) is a. 0.0446 b. 0.9876 c. 0.0221 d. 0.025

A: 9) We need to calculate, P(z&lt;-1.7)

Q: JESTIC True or False: For all n EZ, n +5n +2 is even. True False

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Q: Could you please explain this to me

A: Given, x = 20 degrees in the figure below

Q: 7. 7. Suppose X - N(u.4), which is true?( X- (A) N(0.1): (B) PIX S0} = 4 (C) PIX-u>2; =1-0(1): (D)…

A: Here we use the properties of normal distribution to solve this problem.

Q: 7. In the expansion of px (5+px), the coefficient of the term in x° is 3402. Find the value of p. а.…

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Q: (-1)n+13n (b) n5n n=1

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Q: c) n° n° + 2n is a multiple 3 for all n 2 1.

A: To show: n3+2n is a multiple 3 for all n≥1. Statement used: Principal of Mathematical Induction:…

Q: 1 Σ (-3)²+" (n² + 1) -(4x – 12)" n n=0

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Q: 2. Find the value of 2n=1 Sn=15 2n + 3.

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Q: 5. Given >U, = 3n(n +1) calculate the sum r=1 of ten terms starting from the eighth term.

A: Solution: Given that

Q: 1. Find the coefficient of x5y3 in expansion of the expression (x + 3y)8 2. Sixteen people attend a…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: An algebraic attempt to solve the expression n-1Cn-3 = 21 is shown below. (n - 1)! = 21 2!(n – 3)!…

A: We have to find the error

Q: II (1-) п+1 (for n > 2). 2n i=2

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Q: п d) Σ (-1)" п е n=1 (-1)"*'n² п e) E 2 п +4 n=1 1 Σ- ‚n n=1

A: According to guidelines we can solve only first question. Please submit as separate questions.

Q: The 3rd term in the expansion of (y?+2/y)21 and the 3rd term in the expansion of (y+%)7 are equal.…

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Q: 3. (3 pts) Find a counterexample that shows the following statement is FALSE: S: e*l < (n+1)° is…

A: We want to disprove the following statement by finding the counterexample. Sn: en+1&lt;(n+1)5  is…

Q: (2n + 1)(n² + 1) (e) > (n – 1)(n² – 4)² | n=3

A: The given series is divergent.

Q: 10) Which of the following shows the solution for n2 + 2n 2 24? A) 4十 -6-5-4-3-2-10 123456

A: The given inequality is n2+2n≥24

Q: n²-7n +3 | + 10n-4n2 n2 4 + n3 In (n+2) in(1+4n)

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Q: 8. If n+1, 2n-1 and n+5 are in AP. Find the value of n

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Q: 2" (a) 3 3n+1 (c) E(-1)"; 4n n=1 (b) 3+5n² (4) E n+ n2 n=1 n=1

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Q: 24. There are seven finalists for the Math contest, and medals will be givền tổ thể tốp many ways…

A: Permutation:   It is nothing but the arrangement of items in a definite order where the order is…

Q: 6) If nP3 = 2 nC4 then nC6 = A. 1716 B. 3003 noituloa s ni fluash blud C. 5005 D. 8008

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Q: 3. (P2, Page 19; Write out the Binomial Formula explicitly for n = 3 and n = = 4. Example: For n =…

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Q: A1=3 An=6n+6an-1, for n&gt;1 Find the first four terms

A: We need to put the value n=2, 3, 4 in the given expression which will provide the remaining three…

Q: 2. the number of terms in the expansion of  ( (x+4y)^3(x-4)^3)^2 is? 3. The 5th term of from the…

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Q: e) Un n²-3n+ 1 2n²+1

A: Introduction: A sequence is a collection of functions. This function makes a map from the set of…

Q: 7) For n copies of the book Me and My Sasquatch, a print-on-demand company charges C(n) dollars,…

A: Explanation: The given cost function is: a)  Here we need to find the C(20). Check each piece of…

Q: 10. Use the formula (3k-1)(k-4) = n-5n²-2n, V ne Z* to calculate k-1 20 the sum (-6)+ (-10) + (-8) +…

A: given (-6)+(-10)+(-8)+0+⋯+840+944=∑k=120(3k-1)(k-4)we have given the formula…

Q: 4) Consider the following recursive formula a, = a-1- V3, where n2 2and the first term is a = 12…

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Q: Find the possible values of n. (n2 )" – 2n" + 1 = 0 (n +0,1)

A: We have  n2n-2nn+1=0 and n≠0,1 We can write n2n as n2n=n2n=nn2 So, nn2-2nn+1=0 Let nn=x x2-2x+1=0

Q: 2k +1 S = k-In 2k -1 hint: don't be afraid write it out.., and.. (2n)! (2n - 1)!! = %3D 2" n!

A: Sequence of partial sum is nth term of the series

Q: 20 E(- 1)"2n = n=0

A: Given,           ∑n=020-1n2n