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3. Let n be a positive integer. Prove the following: (i) 13 + 23 + ...+n³ = (1+2+3+..+n)². (Use induction on n) (ii) (Vn e N)(n2 +n+ 7) is odd. (Hint: Consider two cases for n).

3. Let n be a positive integer. Prove the following: (i) 13 + 23 + ...+n³ = (1+2+3+..+n)². (Use induction on n) (ii) (Vn e N)(n2 +n+ 7) is odd. (Hint: Consider two cases for n).

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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3. Let n be a positive integer. Prove the following: (i) 13 + 23 + ... + n³ = (1+2+ 3+ + n)?. (Use induction on n) ... (ii) (Vn e N)(n2 +n+ 7) is odd. (Hint: Consider two cases for n).
Transcribed Image Text:3. Let n be a positive integer. Prove the following: (i) 13 + 23 + ... + n³ = (1+2+ 3+ + n)?. (Use induction on n) ... (ii) (Vn e N)(n2 +n+ 7) is odd. (Hint: Consider two cases for n).
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