Problem 0.7 Consider the sequence an = { 3 1 n² if n = 1 if n ≥ 2 (1) Show that an = (1 n+1 (2) Use part (1) to compute the n-th partial sum sn. (3) Deduce that 1 an converges and state its value. -) for each n ≥ 2.

Q: 3. n-3n+5 n7 Sn=1

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Q: 3. (a) Discuss convergence of the sequence {n} defined by the recurrence relation ₁ = 2 and n+1 = (n…

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A: Basis: Note that T(0)=1, T(1)=2 ,T(2) =2·2 + 1 = 5, T(3) = 2·5 + 2= 12, statement is truefor n…

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Q: 2. Suppose the sequence {sn} satisfies Sn+ 1 - Sn ≤ -1/24 n² For all ne N. Prove that {sn}…

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Q: Given the nth partial sum, find a1, an; and £am. n+2 21. Sn = n+3 an E an ||

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A: SOLUTION:

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Q: let a, b, c, d, four consecutive positive numbers show that g.c.d (a, b, c, d)=1

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Q: 3 For the sequence an = 3" its fifth partial sum S5 its nth partial sum Sn

A: Solved below

Q: 1.11. Question 9 Express each of the following sums in summation notation. (a) x1 y1 x2Y2 + x3Y3 +…

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