5. Prove by induction that for any positive integer n, n i=1 1 n i(i+1) n+1 =

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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5. Prove by induction that for any positive integer n,
6. Prove that
ท
Σ
i=0
=
ท
Σ
1
i(i + 1)
=
n(n + 1)(2n + 1)
6
n
n+1
=
n³
3
+
n
2
+
ท
6
Transcribed Image Text:5. Prove by induction that for any positive integer n, 6. Prove that ท Σ i=0 = ท Σ 1 i(i + 1) = n(n + 1)(2n + 1) 6 n n+1 = n³ 3 + n 2 + ท 6
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