use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. \ 1. 2 + 4 + 6 + · · · + 2n = n(n + 1)2. 1 + 5 + 9 + · ·· + (4n – 3) = n(2n – 1)3. 3 + 4 + 5 + .. + (n + 2) = ;n(n + 5)п (п + 5)4. 3 + 5 + 7 +... + (2n + 1) = n(n + 2)15. 2 + 5 + 8 + · + (3n – 1) =;n(3n + 1)6. 1+ 4 + 7 + · + (3n – 2) = n(3n – 1)

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\ 1. 2 + 4 + 6 + · · · + 2n = n(n + 1) 2. 1 + 5 + 9 + · ·· + (4n – 3) = n(2n – 1) 3. 3 + 4 + 5 + .. + (n + 2) = ;n(n + 5) п (п + 5) 4. 3 + 5 + 7 + ... + (2n + 1) = n(n + 2) 1 5. 2 + 5 + 8 + · + (3n – 1) =;n(3n + 1) 6. 1+ 4 + 7 + · + (3n – 2) = n(3n – 1)

\ 1. 2 + 4 + 6 + · · · + 2n = n(n + 1) 2. 1 + 5 + 9 + · ·· + (4n – 3) = n(2n – 1) 3. 3 + 4 + 5 + .. + (n + 2) = ;n(n + 5) п (п + 5) 4. 3 + 5 + 7 + ... + (2n + 1) = n(n + 2) 1 5. 2 + 5 + 8 + · + (3n – 1) =;n(3n + 1) 6. 1+ 4 + 7 + · + (3n – 2) = n(3n – 1)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.

\ 1. 2 + 4 + 6 + · · · + 2n = n(n + 1)
2. 1 + 5 + 9 + · ·· + (4n – 3) = n(2n – 1)
3. 3 + 4 + 5 + .. + (n + 2) = ;n(n + 5)
п (п + 5)
4. 3 + 5 + 7 +
... + (2n + 1) = n(n + 2)
1
5. 2 + 5 + 8 + · + (3n – 1) =;n(3n + 1)
6. 1+ 4 + 7 + · + (3n – 2) = n(3n – 1)

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