A little challenge

By Tom Brown

Thu, 22 Apr 2021
  • 701 reads
5 comments
 

A problem from my post of Infinite Series, find the sum as just a simple formula (a rational function) of:

1 + 1/4 + 1/9 + 1/16 + ... + 1/n²

Certificate U
Non-fiction
Numbers and Infinities
Miscellaneous

Comments

Submitted by marandina on

If there was an = sign in there I could probably solve it. In this format, you have the better of me, Tom.

 

Submitted by Tom Brown on

Equations? In that case try these. Solve for x ,

2x² + 8 = 0

and what about an equation with more solutions …

1/x + 2/x + 3/x = 6/x

This I learnt in sunday school. I am pleased that you read my mathematics submissions I don't think anybody else does. To be (brutally) honest.

Cheers Paul! Sir Tom Brown

 

Submitted by marandina on

I think the answer to the second equation is x = 1

I am pretty rusty at quadratic equations.

Hoping you are well, Sir Tom. I look forward to more reminiscences about the great country of South Africa. Paul

 

Submitted by Tom Brown on

Thanks Paul something coming up soon.

Your response is interesting. Without the reasoning I think I could just give answers.

The first one the quadratic as you say, has no real solutions x but it does has two imaginary roots. For the second equation each real number x is a solution except for one number x = 0. So that strictly speaking you did have one solution out of the infinitely many.

It's the country music programme tonight.

See you! Goodnight! Mr Brown

 

Submitted by marandina on

Ah yes...any number fits except 0. I did wonder but satisfied myself with the first number that fit rather than following up my instinct that there was more to it. Fascinating stuff.