Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 27E
Related questions
Question
![Prove the following using mathematical induction.
1.
M
13 + 23 + 33 + ... +n' = n°(n + 1)2
4
2.
1.2+2 3+3 4+... + n(n + 1) =
n(n +1)(n+ 2) for any neN
3.
3
2 + 22 + 23 +... + 2" = 2n*1 – 2, for any n eN
4.
5.
1+8+ 16 +... + 8(n – 1) = (2n – 1)2, for any n e N
n(n +3)
6. 1.2.3*2-3-4* 3.4-5** n(n + 1)(n + 2) 4(n + 1)(n + 2)
1
for any neN
...
7.
n? > 2n, for any positive integer n23
8.
3"- 2 2 10n, for any positive integer n 2 4
9.
4° -1 is divisible by 3 for any neN
TA BA
foome
10.
n° + 3n? + 2n is divisible by 6 for any n e N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0db56fc5-2b3a-4b08-827d-2221b63de561%2F51c2d553-c65c-4131-a825-4fff944bff82%2F57dyrdk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove the following using mathematical induction.
1.
M
13 + 23 + 33 + ... +n' = n°(n + 1)2
4
2.
1.2+2 3+3 4+... + n(n + 1) =
n(n +1)(n+ 2) for any neN
3.
3
2 + 22 + 23 +... + 2" = 2n*1 – 2, for any n eN
4.
5.
1+8+ 16 +... + 8(n – 1) = (2n – 1)2, for any n e N
n(n +3)
6. 1.2.3*2-3-4* 3.4-5** n(n + 1)(n + 2) 4(n + 1)(n + 2)
1
for any neN
...
7.
n? > 2n, for any positive integer n23
8.
3"- 2 2 10n, for any positive integer n 2 4
9.
4° -1 is divisible by 3 for any neN
TA BA
foome
10.
n° + 3n? + 2n is divisible by 6 for any n e N
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