21. Prove that for all natural numbers n, ++ + n(n+1) n+1 a. Show it is true for n = 1. Show your work here: b. Assume it is true for n= k. Show your work here: c. Prove it is true for k + 1. Show your work here:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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21. Prove that for all natural numbers n,
1-2
+.. +
2-3
3-4
n(n+1)
n+1
a. Show it is true for n = 1.
Show your work here:
b. Assume it is true for n = k.
Show your work here:
c. Prove it is true for k + 1.
Show your work here:
Transcribed Image Text:21. Prove that for all natural numbers n, 1-2 +.. + 2-3 3-4 n(n+1) n+1 a. Show it is true for n = 1. Show your work here: b. Assume it is true for n = k. Show your work here: c. Prove it is true for k + 1. Show your work here:
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Prove that for all positive integers n, 13+23+33+…+n3=n(n+1)22.

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