use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 13. f + 2° + 3? + ·.. + n² = n(n + 1) (2n + 1)14. f + 23 + 33 + ... + n² =n² (n + 1)?15. 4 + 3 + 2 + ... + (5 – n) = ;n(9 – n)1 (9 — п)(n + 1) = --n(n + 3)16. -2 – 3 – 4 –-... -17. 1.2 + 2.3 + 3•4 + · .. + n(n + 1) = -n(n+ 1) (n+ 2)18. 1.2+3.4 + 5•6+ • · · + (2n –- 1) (2n) =n(n+1)(4n– 1)

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Description: use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 13. f + 2° + 3? + ·.. + n² = n(n + 1) (2n + 1)14. f + 23 + 33 + ... + n² =n² (n + 1)?15. 4 + 3 + 2 + ... + (5 – n) = ;n(9 – n)1 (9 — п)(n

To Prove: 12+22+32+...+n2=nn+12n+16

Answered: 13. f + 2° + 3? + ·.. + n² = n(n + 1)…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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

13. f + 2° + 3? + ·.. + n² = n(n + 1) (2n + 1)
14. f + 23 + 33 + ... + n² =
n² (n + 1)?
15. 4 + 3 + 2 + ... + (5 – n) = ;n(9 – n)
1 (9 — п)
(n + 1) = --n(n + 3)
16. -2 – 3 – 4 –
-... -
17. 1.2 + 2.3 + 3•4 + · .. + n(n + 1) = -n(n+ 1) (n+ 2)
18. 1.2+3.4 + 5•6+ • · · + (2n –- 1) (2n) =n(n+1)(4n– 1)

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