Hi ! Can anybody help me with this?
#Algebra
lucid dust
opal scrollBOT
wooden fulcrum
Hi ! Can anybody help me with this?
is that a 2? in b?
lucid dust
its the letter ,,z"
astral hound
could x be a geometric series?
idk
u could represent it as a geometric series I think...
for 'a' part btw
geometric sequence => u_n = u_1 * r^(n-1)
wooden fulcrum
yeah i think its a geometric series
astral hound
u_1 = sqrt(3)
wooden fulcrum
do u know the forula for sum to n terms for a gp?
astral hound
do u know the forula for sum to n terms for a gp?
if the sequence is converging
then ye
oh wait
we know the end term
2020 right?
1.3
the formula is there
we just need to put what is r and u1
wooden fulcrum
yes
wooden fulcrum
its the letter ,,z"
sum of n terms of a gp is a(1-r^n)/1-r
astral hound
sum of n terms of a gp is a(1-r^n)/1-r
ye
wooden fulcrum
you can plug both of these here
astral hound
since r < 1
wooden fulcrum
yeah
lucid dust
sum of n terms of a gp is a(1-r^n)/1-r
ok, perfect
astral hound
for y it is r>1
wooden fulcrum
i think here we can cancel out some stuff
astral hound
r would be 3 for y
astral hound
man this is the first math problem I m doing after my 12th exams
wooden fulcrum
wait yeah we can
wooden fulcrum
Hi ! Can anybody help me with this?
so yeah write y/x in terms of su of gp
astral hound
afterall if y and x are computed then we could just put it in a calculator lol
and then say the final result is a perfect square
or write some proof for that
wooden fulcrum
itll be i think ((sqrt3(1-(sqrt3)^n)/(1-sqrt3))/(3(1-3^n)/(1-3))
you can factorise (1-3) as (1-sqrt3)(1+sqrt3)
and (1-3^n) can be factorised as (1-(sqrt3)^n)(1+(sqrt3)^n)
and cancel the common factors in numerator and denominator
@lucid dust
wooden fulcrum
grade 10 just got done for me
lucid dust
you just flashed in 4 seconds the whole problem
lucid dust
grade 10 just got done for me
and what age that would be ?
i'm from a different country
wooden fulcrum
and what age that would be ?
15
wooden fulcrum
you just flashed in 4 seconds the whole problem
i think the brackets are confusing you
idk how to type latex stuff
lucid dust
yeah, i need to translate everything on the paper and then see the steps
wooden fulcrum
$$
\frac{\sqrt{3} \times \frac{1-\sqrt{3} n}{1-\sqrt{3}}}{3 \times \frac{1-3^n}{1-3}}
$$
tacit frigateBOT
Renoir
wooden fulcrum
**Renoir**
@lucid dust
wooden fulcrum
thank you
you can factorise this like this:
$$
\frac{\sqrt{3} \times \frac{1-\sqrt{3}^n}{1-\sqrt{3}}}{3 \times \frac{\left(1-\sqrt{3}^n\right)\left(1+\sqrt{3}^n\right)}{(1-\sqrt{3})(1+\sqrt{3})}}
$$
tacit frigateBOT
Renoir
