1. 3 + 6 + 9 + ... + 3n = (3n(n + 1))/2
2. 4 + 4^2 + 4^3 + ... + 4^n = 4/3 ((4^n) - 1)
Use mathematical induction to prove the following statements. Show your work?
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- 3+ months ago by mitchellq...
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- work, statement
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Answers (1)
in·duc·tion
noun
LOGIC
the inference of a general law from particular instances.
MATHEMATICS
a means of proving a theorem by showing that if it is true of any particular case, it is true of the next case in a series, and then showing that it is indeed true in one particular case.
noun: mathematical induction
~google.com
Given: 3 + 6 + 9 + ... + 3n = (3n(n + 1))/2
Equivalent to: (1 + 2 + 3 + ... n) = n(n + 1)/2
Let n=1 then: 1 = 1 x 2/2 = 1
Let n=2 then: 3 = 2 x 3/2 = 2
Do the others the same way.
A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.