1. Show that u1 is divisible by 2. 2. Assume that un is divisible by 2. 3. Show that un+1−un is divisible by 2 (this will require almost no work, just spot something from the first part). 4. Conclude that un+1 is divisible by 2. 5. Write that induction thing.
1. Show that u1 is divisible by 2. 2. Assume that un is divisible by 2. 3. Show that un+1−un is divisible by 2 (this will require almost no work, just spot something from the first part). 4. Conclude that un+1 is divisible by 2. 5. Write that induction thing.
I just did 2(n+2) so must be divisible by 2 haha. By the way how does 3 imply 4?
I just did 2(n+2) so must be divisible by 2 haha. By the way how does 3 imply 4?
Yep, that's correct.
Because if un+1−un=m is divisible by 2 then add un to both sides to get un+1=m+un both terms are divisible by 2 (un is divisible by 2 by assumption) so the sum of two terms which are both divisible by 2 are also divisible by 2 hence un+1 is divisible by 2.
Because if un+1−un=m is divisible by 2 then add un to both sides to get un+1=m+un both terms are divisible by 2 (un is divisible by 2 by assumption) so the sum of two terms which are both divisible by 2 are also divisible by 2 hence un+1 is divisible by 2.
Cheers, mind helping with 4ii as well.
I got 4i to be a circle centre (-1,1) radius root 2. I don't quite get the boundary thing with the second part, what am I looking for?
I got 4i to be a circle centre (-1,1) radius root 2. I don't quite get the boundary thing with the second part, what am I looking for?
4(i) is asking the the locus of points that are exactly (2) away from (1,-1) (surely it's (1, -1) and not (-1, 1))? That is the circle centre (1, -1) and radius (2).
4(ii) is asking for the locus of points that are 2 or less away from (1, -1) but more than 1 away from (1, -1) which is precisely the shaded area inside of the circle between the two concentric circles of radius (2) and radius 1.
4(i) is asking the the locus of points that are exactly (2) away from (1,-1) (surely it's (1, -1) and not (-1, 1))? That is the circle centre (1, -1) and radius (2).
4(ii) is asking for the locus of points that are 2 or less away from (1, -1) but more than 1 away from (1, -1) which is precisely the shaded area inside of the circle between the two concentric circles of radius (2) and radius 1.
A diagram should help:
Yh my bad with 4i. Thats one funky diagram I rate it. So you just want another circle (within the original one) with radius 1 from the centre and shade that bad boy?