Question

How to work this out? (attachment)

Answer 1

The correct answer is marked because i got it wrong.

Answer 2

this is a very very weird way to ask this question
but no matter
the next step is to replace \(k\) by \(k+1\) on the right
on the left add the next term

Answer 3

ok even that was not what they wanted
they wanted you to add the \(k+1\) term to both sides

Answer 4

Like this; 1+5+25+ k+1?

Answer 5

oh no

Answer 6

\[1+5+5^2+...+5^{k-1}+5^{k+1-1}\] is what they want

Answer 7

i replaced \(k\) by \(k+1\)

Answer 8

wow that's it?

Answer 9

a normal person would just write \[1+5+5^2+...+5^{k-1}+5^{k}\]n because \(k+1-1=k\) but no matter

Answer 10

yeah that is it for the left
add the same thing to the right
this is no way to understand induction but whatever

Answer 11

Ooh I always get confused in these. Thanks alot!

Answer 12

yw