The expression 100n² – 1 is equivalent to 1) (10n + 1)(10n – 1) 2) (10n – 1)(10n – 1) 3) (50n + 1)(50n – 1) 4) (50n – 1)(50n – 1)

Q: 18) 5-D*n 5n+2 (-1)".n

A: Given∑n=1∞(-1)n.n(5n+2)Now we apply the series divergence testaccording to series divergence testif…

Q: 7 -1 6 -5 -5 Ax3 = 5 1 1 = 6 1 = 13X3 %3D 0 6 1 1

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Q: 2. * The sum of 8n-3n+10 and -3n? -6n 1) 5n-9n+3 2) 5n -3n- 17 3) -11п*-9п - 17 4) -11n- 3n +3

A: To find the sum of 8n^2-3n+10 and -3n^3-6n-7.

Q: 10 5n² + 5n + 2 an 5n5 + 6n + 3/n, k =

A: Given a series . We need to find a number 'k'. Let's start.

Q: s(-1)n-1 In(4n + 5) 7 = 1

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Q: 1. Prove that for any n > 2, n E N, one has (1-)(--)(--) - (-) - n +1 2n

A: I have solved question no. 1 according to policy rule.   To solve q.1, I have used method of…

Q: find the 4th term of (2n^2-3m)^4

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Q: Find the sums of the series in Exercises

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Q: 2. + -+- 1.3 3.5 5.7 + + 1 n (2n-1)(2n+1) 2n+1

A: As per guidelines, I can do first question only.

Q: { :Find the first 3 terms for 2n-1 (2n-1)! (−1)n+¹

A: given sequence  -1n+1x2n-12n-1!

Q: 4.) -8n + 4(1 + 5n) %3 -бп — 14

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Q: 14. -13 < 3 + 8p < 11 -8 -6 -4 -2 0 6 8 Interval Notation:

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Q: 3.5n 7n+1 n=1

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Q: 3- 2 GL 1- 7654 321 42345 67 -1- -3 723

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Q: Does -3(4n + 2) = 4n + -2(4n - 6) have a solution or no

A: We have to find whether this equation has solution or not. The given expression is -3(4n + 2) = 4n +…

Q: Find an explicit formula for 1/(2-1/2), 2/(3-1/3),3/(4-1/4),4/(5-1/5)...

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Q: 8n +7 = 31 10 - 6v = -104

A: Let the given equation is 8n + 7 = 31 Subtract 7 from both sides 8n +7 - 7 = 31 - 7 8n = 24 Divide…

Q: 3.5.7 . (2n+1) If an thenlim a =? 2.5.8. (3n-1) ans. 2. 8. 1.

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Q: ∑ n=1    1/9n^2-18n+8

A: Given ∑n=119n2-18n+8Now lets substiute n=1 and solve

Q: How many terms will be in the expansion of (x – 8y)*" ? There will be 10 – 1 = 9 terms in the…

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Q: 2) 2° +2¹+2²+...+ 2n = 2n+¹ -1 Remember: 2⁰=1

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Q: . 2+ 4 +6+8+ 10 + ·… + 2n = n+ n² . 1+8+ 27 + .. + n³ = n² (n + 1)2 2+5+8+ ... + (3n – 1) = ;n(3n +…

A: Here is the solution of the given problem. Mathematical Induction Method:

Q: 1 Σ (2n – 3(2n – 1) n=1

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Q: Find (2n – 3)(n + 4). * О Зn +1 О 2n^2 + 5n -12 О 2n^2- 12 О 2n^2 + 11п +1 Simplify: 2a^2(5а- 6) -…

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Q: 1. Solve: An = An -1+ n; Ao = 0

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: 2.8) Mathematics - Expand and explain the steps involved. * i) (3x4 – 7)(-4.x³ + 15) i) (2a8 — Згр)2…

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Q: 19. Algebra If mZRZT- 110, mRZs-36, and MZTZS- 8, what are mRZS and mTZS?

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Q: 14 = 0 23. -x2 + 2x + 24 = 0 = -81 25. 2x2 – 8x = –32 - 15 = 4 27. -3x? – 7+ 2r = -11

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Q: 4. 9.6 = 1.26 5. 0.75a = -9 6. -413.4 = -15.9n

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Q: 1/3 27X2-43 446 y and write your final 8/3-17/6 хочу anmyn. Then enter your a, mand n

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Q: 17. lim 12n+9 5n - 1 12

A: Consider the given limit  limn→∞5n-112n+9

Q: 3n + 14 = -4

A: To solve the given equation for 'n'.3n+14=-4

Q: (– 1)n+1x2n+2 n=1 3n+1(2n+ 1)! (– 1)"-1x²n-1 Σ n=1 30-1(2n - 2)! Some other answer (– 1)"+1x2n+3 Σ…

A: We have to choose the correct answer from the given option

Q: 0 2५+ 3५-2५-० 24 +4== 364-3647134-

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Q: 4 1 -12-11-10-9 -8-7 -6 -5 -4 -3 -2 -1 1/2 3 4 5 7 8 9 10 11 12 -2 -4 -5 -6 -7 -8 -9 -10 -11 -12 987…

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Q: Evaluate (1-i)^⅛ 1.0392 + 0.1024i 1.0392 - 0.1024i 0.1024 - 1.0392i 0.1024 + 1.0392i

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Q: 4 (a) Write out the multiplication table for Z6. How many times does [0]6 appear in each row of the…

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Q: 11. 6v + 38 < -4 or 2(v + 3) 2 -2 +++++ -8 -6 4 -2 0 2 4 6 8 Interval Notation:

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Q: 8. Ση-0 ne-1 4n 9. En=0 (n+2)3 n=0 (n+2)³ 3. 10. Σ0 n-3n+2 %30 n2-3n+2

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Q: 5 Σ (3n + 2)(2n – 1) n = 3

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Q: If Z1=2-4i and Z2= -π+5i Find 1. (Z1+Z2) 2. (Z2-Z1) 3. (Z1-Z2)

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Q: 2n+5 00 Zn=1 3n

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Q: 6 - 22n-1 5n+1 n=1 =D1

A: Given: ∑n=1∞6×22n-15n+1 A ∑n=1∞fn series is convergent if, fn+1fn&lt;1 Check the convergence of the…

Q: Use mathematical induction to prove

A: Given that,

Q: The sum of 8n^2-3n+10 and -3n^2-6n-7

A: Sum of 8n2-3n+10 and -3n2-6n-7       = 8n2-3n+10 + (-3n2-6n-7)        We will add given expression…

Q: 12 - 2 Let Ax) = x² + 3x + 5 , and 1 A = -2 1 3 3 -1 Which one is (A)=?

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Q: 7) -13 =- 12 8) -5 +-11 10 9) 252 =-11n + 10 10) 189 = -1 + 10m

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Q: 13) b - 6b + 8 14) n + 6n + 8 15) 2n + 6n - 108 16) Sn' + 10n + 20

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.