Prove that the finite sum rule ∑ k = 1 n ( a k + b k ) = ∑ k = 1 n a k + ∑ k = 1 n b k holds for every positive integer n .

Question

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Answer 1

Question

Chapter A.2, Problem 11E

(a)

To determine

Prove that the finite sum rule ∑k=1n(ak+bk)=∑k=1nak+∑k=1nbk holds for every positive integer n.

(b)

To determine

Prove that the finite sum rule ∑k=1n(ak−bk)=∑k=1nak−∑k=1nbk holds for every positive integer n.

(c)

To determine

Prove that the finite sum rule ∑k=1ncak=c⋅∑k=1nak holds for every positive integer n.

(d)

To determine

Prove that the finite sum rule ∑k=1nak=n⋅c holds for every positive integer n if ak has the constant value c.

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Answer 2

Question

Chapter A.2, Problem 11E

(a)

To determine

Prove that the finite sum rule ∑k=1n(ak+bk)=∑k=1nak+∑k=1nbk holds for every positive integer n.

(b)

To determine

Prove that the finite sum rule ∑k=1n(ak−bk)=∑k=1nak−∑k=1nbk holds for every positive integer n.

(c)

To determine

Prove that the finite sum rule ∑k=1ncak=c⋅∑k=1nak holds for every positive integer n.

(d)

To determine

Prove that the finite sum rule ∑k=1nak=n⋅c holds for every positive integer n if ak has the constant value c.

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Answer 3

Question

Chapter A.2, Problem 11E

(a)

To determine

Prove that the finite sum rule ∑k=1n(ak+bk)=∑k=1nak+∑k=1nbk holds for every positive integer n.

(b)

To determine

Prove that the finite sum rule ∑k=1n(ak−bk)=∑k=1nak−∑k=1nbk holds for every positive integer n.

(c)

To determine

Prove that the finite sum rule ∑k=1ncak=c⋅∑k=1nak holds for every positive integer n.

(d)

To determine

Prove that the finite sum rule ∑k=1nak=n⋅c holds for every positive integer n if ak has the constant value c.

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Answer 4

Question

Chapter A.2, Problem 11E

(a)

To determine

Prove that the finite sum rule ∑k=1n(ak+bk)=∑k=1nak+∑k=1nbk holds for every positive integer n.

(b)

To determine

Prove that the finite sum rule ∑k=1n(ak−bk)=∑k=1nak−∑k=1nbk holds for every positive integer n.

(c)

To determine

Prove that the finite sum rule ∑k=1ncak=c⋅∑k=1nak holds for every positive integer n.

(d)

To determine

Prove that the finite sum rule ∑k=1nak=n⋅c holds for every positive integer n if ak has the constant value c.

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Answer 5

Chapter A.2, Problem 11E

(a)

To determine

Prove that the finite sum rule ∑k=1n(ak+bk)=∑k=1nak+∑k=1nbk holds for every positive integer n.

(b)

To determine

Prove that the finite sum rule ∑k=1n(ak−bk)=∑k=1nak−∑k=1nbk holds for every positive integer n.

(c)

To determine

Prove that the finite sum rule ∑k=1ncak=c⋅∑k=1nak holds for every positive integer n.

(d)

To determine

Prove that the finite sum rule ∑k=1nak=n⋅c holds for every positive integer n if ak has the constant value c.

Answer 6

Chapter A.2, Problem 11E

(a)

To determine

Prove that the finite sum rule ∑k=1n(ak+bk)=∑k=1nak+∑k=1nbk holds for every positive integer n.

Answer 7

Chapter A.2, Problem 11E

(a)

To determine

Prove that the finite sum rule ∑k=1n(ak+bk)=∑k=1nak+∑k=1nbk holds for every positive integer n.

Answer 8

(b)

To determine

Prove that the finite sum rule ∑k=1n(ak−bk)=∑k=1nak−∑k=1nbk holds for every positive integer n.

Answer 9

(b)

To determine

Prove that the finite sum rule ∑k=1n(ak−bk)=∑k=1nak−∑k=1nbk holds for every positive integer n.

Answer 10

(c)

To determine

Prove that the finite sum rule ∑k=1ncak=c⋅∑k=1nak holds for every positive integer n.

Answer 11

(c)

To determine

Prove that the finite sum rule ∑k=1ncak=c⋅∑k=1nak holds for every positive integer n.

Answer 12

(d)

To determine

Prove that the finite sum rule ∑k=1nak=n⋅c holds for every positive integer n if ak has the constant value c.

Answer 13

(d)

To determine

Prove that the finite sum rule ∑k=1nak=n⋅c holds for every positive integer n if ak has the constant value c.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. A.2 - Assuming that the triangle inequality holds for...Ch. A.2 - Show that if r ≠ 1, then for every positive...Ch. A.2 - Prob. 3E Ch. A.2 - Prob. 4E Ch. A.2 - Show that for all positive integers n. Ch. A.2 - Prob. 6E Ch. A.2 - Prob. 7E Ch. A.2 - Show that 2n ≥ 1/8 for n ≥ –3. Ch. A.2 - Sums of squares Show that the sum of the squares...Ch. A.2 - Sums of cubes Show that the sum of the cubes of...

Prove that the finite sum rule ∑ k = 1 n ( a k + b k ) = ∑ k = 1 n a k + ∑ k = 1 n b k holds for every positive integer n .

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Prove that the finite sum rule ∑k=1n(ak+bk)=∑k=1nak+∑k=1nbk holds for every positive integer n.

Prove that the finite sum rule ∑k=1n(ak−bk)=∑k=1nak−∑k=1nbk holds for every positive integer n.

Prove that the finite sum rule ∑k=1ncak=c⋅∑k=1nak holds for every positive integer n.

Prove that the finite sum rule ∑k=1nak=n⋅c holds for every positive integer n if ak has the constant value c.

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