Sequence induction proof (1 Viewer)

[MoonMonster196884]

A sequence is defined by and . Prove that for each n:

 

[Drongoski]

In outline as LaTeXing is so tedious.



Therefore true for k = 1. Now assume true for n = k (k >= 1)



i.e. if true for n=k true also for n=k+1

. . . blah ... blah ... blah . . .

 

[MoonMonster196884]

it's very easy i did it.
Assume $b_{k}=1+\sum_{r=1}^{k-1}b_{r}^{2}$
RTP that for k+1
We know $b_{k+1}=b_{k}\left(b_{k}+1\right)$
=$b_{k}^{2}+b_{k}=b_{k}^{2}+1+\sum_{r=1}^{k-1}b_{r}^{2}$ by assumption
=what we were RTP