Finding Equivalent resistance

so, R_eq=R+ R//kR_eq= R+ 11R+1kR_eq

solve this equation for R_eq

hope this clears ur doubts

consider this problem...

we have to find equivalent resistance of this infinite arrangement of resistors...

here the system extends till infinity....

the building block of the system is recognised as

now if we detach the first buiding element, we get something like this...

thus the original system equals frst building block + rest of the network...

now if we look carefully, the rest of the network has ∞-1 i.e ∞ no of building blocks....
thus if we measure equivalent resistance about the rest network then it will give (very very very very very very very nearly) same equivalent resistance as the full network and let this eq resis be R_eq

thus we write the network as..

from there we get R_eq= R + R//R_eq

(+) signifies series connection and (//) signifies parallel connection,

i.e, R_eq=R+R. R_eqR+R_eq
→ R_eq² - R² - R. R_eq = 0

solving we get, R_eq= R+√R²+4R²2

this is what we apply to get equivalent resistance for such infinite extensions....

now lets get closer to our question...

consider this connection,

using this i think we can assert that in the original question, the rest of network has a resistance of kR_eq.