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Let tn be the n-th triangular number, starting with t1 = 1, t2 = 3, t3 = 6, %3D %3D etc. (a) Prove that tn n(n+1) (b) Show that t-1+t = t„2 . (c) Prove that (1/t,) = 2 . n=1 Hint: Use the fact that 1) 1 - n{n+1) n+1

Let tn be the n-th triangular number, starting with t1 = 1, t2 = 3, t3 = 6, %3D %3D etc. (a) Prove that tn n(n+1) (b) Show that t-1+t = t„2 . (c) Prove that (1/t,) = 2 . n=1 Hint: Use the fact that 1) 1 - n{n+1) n+1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let tn be the n-th triangular number, starting with t1 = 1, t2 = 3, t3 = 6, %3D %3D etc. (a) Prove that tn n(n+1) (b) Show that t-1+t = t„2 . (c) Prove that (1/t,) = 2 . n=1 Hint: Use the fact that 1) 1 - n{n+1) n+1
Transcribed Image Text:Let tn be the n-th triangular number, starting with t1 = 1, t2 = 3, t3 = 6, %3D %3D etc. (a) Prove that tn n(n+1) (b) Show that t-1+t = t„2 . (c) Prove that (1/t,) = 2 . n=1 Hint: Use the fact that 1) 1 - n{n+1) n+1
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