Clap your hands say yeah right

Music lovers, check this out: www.meltingspot.se.

Det här är fanken bland de bästa beslut vi tagit: http://www.linasmatkasse.se/.
Varannan vecka två kassar med bra matvaror (ekologiskt och kravmärkt till stor del) och 5 medföljande recept, hem till dörren. Goda & varierande recept dessutom! En tidsbesparare.

Så ikväll … låt mig se vad Lina har bestämt … blir det Lammfärsbiffar med varm aubergine- och fetaröra och klyftpotatis.

Here is a variant of this proof:

(… and sorry for the fact that it is jotted on a piece of paper & that the image quality is crap. I am at the nursery this week (trying to get my son compatible with the routines there) and I only have an iPhone at my disposal)

UPDATE: I was a bit sloppy when writing down the proof. Not only is it written in Swedish … it also contains two small typos. The denominators which are written as 2:s should of course have been squared too. They should be 4:s …

UPDATE 2: I was asked for some clarifications. Here we go:

Let C_n be the sum of the cube-series at n.
Let S_n be the sum of the squared series at n.

If C_n and S_n grows with the same delta for each n, then C_n = S_n for all n.

The delta for C_n between n and n-1 is:
C_n – C_n-1 = n³ (trivial).
The delta for S_n between n and n-1 is:
S_n – S_n-1 = … = … = n³ (as shown on the paper on the photo).

Hence C_n = S_n for all n.

DAG 0:

DAG 1:

DAG 2:

DAG 3:

DAG 4:

DAG 5:

Andra bosättare:

DAG 6:

DAG 7:

DAG 8:

DAG 9:

DAG 10:

DAG 11:

DAG 12:

DAG 13:

DAG 14:

DAG 15:

(klicka för större bilder)

Fortsättning följer.