Suppose {xn} is increasing and has a subsequence {xnk} which converges to L. We will prove that {xn} itself converges to L.
For any ϵ>0, we want to find an integer Nϵ such that |xn−L|≤ϵ for any n≥Nϵ.
Since {xnk} is increasing and converges to L, we can find kϵ such that for any k≥kϵ, −ϵ<xnk−L<0.
Take Nϵ=nkϵ, then for any n≥Nϵ, xnkϵ≤xn≤L, so −ϵ≤xnkϵ−L≤xn−L≤0.
Similarly, we can prove when {xn} is decreasing
18= (d - 0.25d) - 0.25d
18= 0.75d - 0.25d
18= 0.50d
d = 36
the original price was $36
Answer:
love his music... absolutely insane
Step-by-step explanation:
my favorite song is paid my dues my nf. One reason why I like it is because I can relate closely to it. it also gives a really chill but dark vibe. I think this song is supposed to be about how the rapper, nf just wants a regular life with regular friends.
D on both ...................
The actual reduced ratio is 7:2