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6.25. every integer n> 4. - 9n - 10) for every nonnegative integer n.l Prove that 1++++ <2- for every positive integer n. ... Exercise 46 of Chant

6.25. every integer n> 4. - 9n - 10) for every nonnegative integer n.l Prove that 1++++ <2- for every positive integer n. ... Exercise 46 of Chant

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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Help me with 6.26

6.26. Prove that 81 | (10"+1 627. Prove that1+ ++.. 00 In Exercise 4.6 of Chapter 4, you were asked to prove that if 3 | 2a, whe this result is true. Prove the following generalization: Let a e Z. For eve 9n - 10) for every nonnegative integer n. +<2- for every positive integer n. 3 | a. 29. Prove that if A1, A2, ..., An are any n > 2 sets, then A1 N A2 n... An = A1 UA2 U...U 6 30. Recall for integers n > 2, a, b, c, d, that if a = b (mod n) and c = d (m Cnra+c= b+d (mod n) and ac = bd (mod n). Use these results and ma following: For any 2m intégers a1, a2, ..., am and b1, b2, (a) a1 +a2 + + am = b1 + b2 + . .+ bm (mod n) and w (b) aja2am = bib2 ... bm (mod n). d 091 5.31. We saw in Exercise 5.7(a) that (a + b)(+) > 4 for every two posi t r ovoi og odisM to olgia a. every n > 1 positive real numbers a1, a2, ..., an that i3D1
Transcribed Image Text:6.26. Prove that 81 | (10"+1 627. Prove that1+ ++.. 00 In Exercise 4.6 of Chapter 4, you were asked to prove that if 3 | 2a, whe this result is true. Prove the following generalization: Let a e Z. For eve 9n - 10) for every nonnegative integer n. +<2- for every positive integer n. 3 | a. 29. Prove that if A1, A2, ..., An are any n > 2 sets, then A1 N A2 n... An = A1 UA2 U...U 6 30. Recall for integers n > 2, a, b, c, d, that if a = b (mod n) and c = d (m Cnra+c= b+d (mod n) and ac = bd (mod n). Use these results and ma following: For any 2m intégers a1, a2, ..., am and b1, b2, (a) a1 +a2 + + am = b1 + b2 + . .+ bm (mod n) and w (b) aja2am = bib2 ... bm (mod n). d 091 5.31. We saw in Exercise 5.7(a) that (a + b)(+) > 4 for every two posi t r ovoi og odisM to olgia a. every n > 1 positive real numbers a1, a2, ..., an that i3D1
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