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Mathmatical induction 2

0 votes

12 + 42 + 72 + ... + (3n - 2)2 = quantity n times quantity six n squared minus three n minus one all divided by two

asked Jul 31, 2014 in PRECALCULUS by Tdog79 Pupil

2 Answers

0 votes

imagequantity n times six n squared minus three n minus one all divide by two.

image

Mathematical induction is a special way of proving things.

It has only two steps.

Step - 1) Statement is true for n = 1

Step - 2) one part being assume the statement is true for n =  k

prove the statement is true for " k + 1"

Check the equation for n = 1

Left hand side

image

                 image

                 image

Right hand side

image

                                image

                               image

For n = 1, the statement is true.

  • Assume the statement is true for n =  k

image

  • Now, prove the statement is true for " k + 1".

For n = k + 1

The statement is image ---> (1)

We need to the prove the equation (1).

answered Jul 31, 2014 by david Expert
0 votes

Contd...

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 Add image on each side.

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Therefore, by the mathematical induction the statement is true.

 

answered Jul 31, 2014 by david Expert

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