Question

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.

Answer 1

Sn: 12 + 42 + 72 + . . . + (3n - 2)2 = (n(〖6n〗^2-3n-1))/2

Answer 2

My starting S1:1^2+4^2+7^2+…+(3*1-2)^2=1(6*1^2-3n-1)/2 is it correct?

Answer 3

Sn= Values of n will change from 1-4 ? and what come sin between something is wrong with this i gues?

Answer 4

you want to do the basis case

Answer 5

didn tget it sorry could u explain

Answer 6

You want to prove the following set of statements (infinite set of statements)

S1: 1^2 = 1 (6*1^2-3*1-1))/2

S2: 1^2 + 4^2 = 2 (6*2^2-3*2-1))/2

S3: 1^2 + 4^2 + 7^2 = 3 ( 6*3^2 - 3*3 -1 ) /2

... and so on

In general you want to prove that the nth statement

Sn : 1^2 + 4^2 + 7^2 + ... + (3n-2) ^2 = n ( 6*n^2 - 3n - 1) / 2

is true for all n, positive integers n=1,2,3,...

Answer 7

thanks alot so should i do it with 4 and add them?

Answer 8

S1:1^2+4^2+7^2+…+(3*1-2)^2=1(6*1^2-3n-1)/2
S1: 1^2 = 1 (6*1^2-3*1-1))/2
S2: 1^2 + 4^2 = 2 (6*2^2-3*2-1))/2
S3: 1^2 + 4^2 + 7^2 = 3 ( 6*3^2 - 3*3 -1 ) /2 ...

and S4:1^2+4^2+7^2=(3*4-2)^2=4(6*4^2-3*4-1)/2