Prove 1 u <mrow class="MJX-TeXAtom-ORD"> 0 </m

Sattelhofsk

Sattelhofsk

Answered question

2022-06-14

Prove 1 u 0 u 1 + 1 u 1 u 2 + + 1 u i u i + 1 + + 1 u n u n + 1 = n + 1 u 0 u n + 1

Answer & Explanation

svirajueh

svirajueh

Beginner2022-06-15Added 29 answers

In case you were wondering how kmitov's comment came about, note that d = u 1 u 0 = u 2 u 1 = . . . = u n u n 1
LHS = 1 u 1 u 0 u 1 u 0 u 1 u 0 + 1 u 2 u 1 u 2 u 1 u 2 u 1 + . . . + 1 u n + 1 u n u n + 1 u n u n + 1 u n
= 1 d ( 1 u 0 1 u 1 ) + 1 d ( 1 u 1 1 u 2 ) + 1 d ( 1 u 3 1 u 2 ) + . . . + 1 d ( 1 u n 1 u n + 1 )
Factoring out the 1 d , the reciprocals cancel out to give LHS = 1 d ( 1 u 0 1 u n + 1 )
= 1 d ( u n + 1 u 0 u n + 1 u 0 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?