Question

Can anyone help me solve this? 1^2 + 4^2 + 7^2 + ... + (3n - 2)^2 = quantity n times quantity six n squared minus three n minus one all divided by two

Answer 1

I already found n=1. i'm just having some trouble with n=k n=k+1

Answer 2

i solved the left side i just don't know what to do with that fraction on the right

Answer 3

ok

Answer 4

@Mokeira do you think you can help me please?

Answer 5

what is in between 7^2 + ... + (3n - 2)^2

Answer 6

there's nothing in between those just those ellipses

Answer 7

i set it up to n=1 and got true

Answer 8

ok..let me try it

Answer 9

okie doks :)

Answer 10

does the quantity n multiply six n squared or everything?

Answer 11

I'll set it up sorry about that

Answer 12

(n(6n^2-3n-1))/2 that's the right side

Answer 13

ok..great!

Answer 14

@dg2

Answer 15

https://in.answers.yahoo.com/question/index?qid=20120915100601AAnfIHw

Answer 16

but idk if i should add the fractions together

Answer 17

@ApollosChariot

Answer 18

@midhun.madhu1987

Answer 19

formula i think 1/6n(n+1)(2n+1)

Answer 20

there's no formula...i got up to here:6k^3-3k^2-k/2 +(3k+1)^2

Answer 21

How did you get that?

Answer 22

that's not how you do it tho but thanks for trying I appreciate it

Answer 23

This is related to Principle of mathematical induction.

The various steps to prove it are:

1. Prove it for n=1.
2. Assume it is true for n=k.
3. Then we prove n=k+1 for every n=k.

As an example, please find the attached file written by me to solve these kinds of questions... let me know if you need any help or clarifications...

Answer 24

okay thanks I finally understand

Answer 25

hey @midhun.madhu1987 when you are proving for P(1) you only use n, why dont you use 2+4+6?

Answer 26

Because if the value of n=1, then it contains only one term.. that is 2n.

Answer 27

yeah...i have understood :)