M/c Select the mathematical expression that is equivalent to the sum n– 4 j+7 n – 5 + (n – 4)n+3 nn - 5 E *7+ jn+3 i+7 -3 O E=*7+ j*3 - 3 ο Σ 7+ (n- 40+3. i+7

Q: +1++4+ +7++10 written in sigma notation is equal to The sum 3k-5 A k=1 3k - 4 B k=1 3k-2 k=1 3k-1…

A: Let's find.

Q: 2 Look at the following picture. 000 000 1st term 2nd term 3rd term Prove that the number of…

A: Given:

Q: 1-4 In z S(z) = 1+4 In z Bring your answer to the simplest possible form.

A:

Q: 2. Find the formula of the general n th term . (i) (1,3,5,7,.) (1 2 3 4 (ii) 2 3 45" 11 (iii) 48 16'…

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

Q: 2 3 n a. If n E N, then + + + •+ 3! 4! (n+1)! (Hint: 3! (reads 3 factorial) = 3 x 2 x 1. n! = nx…

A: Induction theory: Let the given statement is P(n). Step-1: We need to check P(n) is true for n=1.(or…

Q: The solution of e² = -2 for n = 0,±1,±2,. is %3D ... Select one: O a. In2 + in(1+n) O b. In2 +…

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Q: 19 (a) Solve In(2r)-3 In(z) 0 for r. (b) Use the following table to find the value of z from 7a-2-…

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Q: 5) Show that n(n+1)(4n-1) E"=1 r(2r – 1) 6 Hence find E015 r(2r – 1) |

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Q: 1 1. n=1 /n 00 2. E ne ne n? n=1 3. n(In(n))2 sin (7n) 4. n2 n=1 5. Vn n1- 2 6. 3.

A: Note: " since you posted multiple question. As per our guidelines we are supposed to solve one at a…

Q: (-1)"n2n+1 n=0 32n-1(2n+ 1)! The sum of the series is 3 18 O 9/3 1 18 tan() 3 9 tan Click Save and…

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Q: fond the value of the double sum

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Q: The inductive step of an inductive proof shows that for k > 0, if E 2' = 2k+l – 1 then E 2 = 2*+2…

A: We have to prove for k≥0, If ∑j=0k2j=2k+1−1 then ∑j=0k+12j=2k+2−1 by inductive step. The proof is…

Q: Given: In(1+x) = >) (-1)". -xn+1 if |x| < 1. n+1 n=0 Compute the exact value of -1)"(n+2) 2n+1(n +…

A: Given: ln(1+x)=∑n=0∞(-1)nn+1xn+1 where x&lt;1To Compute: Exact value of ∑n=0∞(-1)n(n+2)2n+1(n+1)

Q: 6. The series 4(4) – 8(6) + 16(8)- 32(10) + 64(12) – 128(14) + 256(16) – 512(18) is represented by…

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

Q: (-1)"(n + 2) 2n+1(n + 1) 4. Compute the exact value of n=0

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Q: Write out the sum. n- 1 1 Σ 5k+1 k = 0 Find the first, second, third and last terms of the su n- 1 1…

A: Q 1)- ∑k=0n-11/5(k+1)   Q 2)-∑k=0n1/9k

Q: The coefficient recursion relation for the solution Y1 = E an x"+1 of the %3D n=0 equation x2y" –…

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Q: 7. Given u, = 3n(n +1)² find r=1 i. The summation of fifteen terms starting from the seventh term

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Q: Prove by Math Induction - 1· 3 + 2 · 4 + ... n(n+2) = n(n+1)(2n+7) to Step 1: Verify Step 2:…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: (-1)"(п + 2) 2n+1(n +1) Compute the exact value of n=0

A: The geometric series formula is ∑n=0∞rn=11-r, where r&lt;1. Simplify the numerator of the given…

Q: k ak ak a-1,a +1 (-1)* 1/½(-1)*+1 kak 4), a +1 a- (ak + b)(n) (ak+b)(n+1) a(n+1)

A: ∆ak= ak+1-ak      = ak(a-1) therefore anti difference of ak=ak/(a-1)

Q: 16. prove that Edn 2(d) = 2u(n). 17. prove that Edn H(n/d)T(d) = 1 and Edn H(n/d)o(d) = n for all n,…

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Q: 2. Let, a1= 3 and for n ≥ 2, an = 2an-1 + 1, express an in terms of n. for n ≥ 3, an = 2an-1+ bn-1…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

A: The solution is given as

Q: (-1)"(n+ 2) 2n+1(n + 1) 4. Compute the exact value of n=0

A: Given series is  ∑n=0∞-1nn+22n+1n+1

Q: 5 u 2 x -3 A = у 7 C = -4 D = 6 1 -2 1 -8- Find N = AC - D, if defined. Give N12 OA. operation…

A: Given: A=2x-3y7-4,   C=-5u-21v6,   D=5-76-8 AC=2x-3y7-4·-5u-21v6…

Q: all n N we have We apply this successively for n = bn+1 bn N, N+1, n 9 bN+1 < (m + €)bN bN+2 < (m+…

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Q: a(1 – rª ) n³(1-0.5'g(n) ; (1 – r) (1-0.5) (n³ – n³+0.5!g(n)) 0.5 =(2n3 – – 2n² ) 2 * n³ * 0.5'g(n))…

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Q: cos(n") In(4) 1. 1 2. n In(n) n%3D 6n + 3 (-1)" n=1 1 4. n - 5 3.

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Q: (k² – k) = O a. n? O b. n(n + 1)(2n + 1) O c. 6n + (n +1)(2n + 1) O d. (n + 1) O e. 플 (12-1) O f. 00…

A: the given expression is: ∑k=1n k3-k we have to find the value of the given expression.

Q: 2 3 -1 Let A = 3 2 Find M23- 1 3 1 O 3 O11 O-3 O-11

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Q: Please help I’m stuck on this one, I’m stuck

A: Introduction: Big-O notation analysis on polynomial function: If f(n)=a0+a1n1+a2n2+...+amnm, then…

Q: '글 +2+글 +5 The sum +8+ +11 written in sigma notation is equal to 8 3k-2 A k=1 2 8 3k - 1 B k=1 8 3k…

A: The sum 1/2 +2+7/2 +5+13/2 +8+19/2 +11.

Q: Find L {(2 t" - 3) (t +2)} O 2(2n)! n! -- $2n+1 sn+1 O 2(2n)! s2n+1 n! sn+1 O 2(n²!) n²+1 n! sn+1 O…

A: To find:- L{(2tn-3) (tn+2) }

Q: n=1 B. E(-1)"- In n n=2 1 Inn c.(-1)"+1. n- Inn (-1)*+1. n + n=1 E.(-1)" sin(n) n=1 E(-1)"- n=2…

A: This is a problem of series calculation. based on the several available tests we can determine which…

Q: which ones n 3n +2 have the Σ 2n + 3 n=2 same character ? n-1 4 3 n° +2 III. > 3 n° +3 1. E: II. E…

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Q: 5-4cos(n) %3D and bn 9. %3D n2 Let an n2+1

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Q: ¸1(1 + r)n−¹ − 1. (n-1-1₁ r Sn (1+r)"So - P[- =

A: Sn = 1+rnS0 - P1+rn-1-1rAim: To find expression for 'n'.…

Q: [1 1 1 If A = 1 1 3"-1 3"-1 3"-1 prove that A" =| 3"-1 %3D 1 1 3"-1 for 1 3"-1 all values of n e N.…

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Q: 1 1) Σ n=2 nlnn a : (doğ b) d) 1 e) -1 E 1nªe-n² -n=1 (doğnu)

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Q: Find L {(2 t" – 3) (t + 2)} 2(2n)! s2n+1 sn+1 O 2 (2n)! $2n+1 n! sn+1 4 n! 82n+1 n! n+1 8. O 2(n²!)…

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Q: Find a formula for sn, n > 1, if sn is given by 4 5 7 8 8' 11' 14' 17 Sn =

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Q: 5 (a) Consider the positive integer s = 23n-1. n=2 (i) Express s as a sum without using E-notation.…

A: Given sequence is  s=∑n=2523n-1

Q: N(N+1) N²(N+1}? and ΣΜ N(N+1)(2N+1) Use linearity and the formulas E j = N to evaluate the sum. 44…

A: The sum is ∑j=044jj-1. Rewrite the sum as follows.…

Q: -1 M = 6. Find formulas for the entries of M", where n is a positive integer. M" =

A: To Find formulas for the entries of M^n, where n is a positive integer

Q: Therefore n-1 ( fsi+4P + föi+3h foi+3P + fei+2h ) (foi-19+ fei-2k , feiq + fei-1k Tên-3 = k| i=0…

A: Given : In Theorem 4,                 fmm=-1∞=1, 0, 1, 1, 2, 3, 5, 8, ......... We need to explain…

Q: 7. E(-1)"- Vn +1 n=1

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Q: n +1 5n An bn n + 2' 4n2 – 3' { 400/n -1/(400n2) n even { Į 7 n/(1+n²) 1 901 п оdd Cn dn

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Q: (k-k) = O a. n O b. 6n +(n + 1)(2n +1) OC. 00 O d. (n + 1) O e. 4(n + 2) (n² - 1)

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Q: 37 4 + 3 8 3n 3 + n -10 = 3 n -12+ that show (A+2) 2 2n3 + 2-10 da by hrst expressing b) hence…

A: We know that, The Power rule: ∫ax+bndx=ax+bn+1an+1+C  ; n≠-1 (a). We have to show:…