please help me with SEQUENCE problem. attachment

Question

anonymous · Answer

$$sequence:  a_1 = \frac{ 1 }{ 2 }, a_{n+1}=\frac{ 4n-1 }{ 3n+2 }a_n$$
(a) Determine: $$S_2 = a_1 + a_2$$


(b) Determine convergence, divergence of $$\sum_{?}^{?} a_n $$ by the ratio test

anonymous · Answer

hi do you see what  i posted?

anonymous · Answer

$$sequence:  a_1 = \frac{ 1 }{ 2 }, a_{n+1}=\frac{ 4n-1 }{ 3n+2 }a_n$$
(a) Determine: $$S_2 = a_1 + a_2$$


(b) Determine convergence, divergence of $$\sum_{?}^{?} a_n $$ by the ratio test

anonymous · Answer

$$sequence:  a_1 = \frac{ 1 }{ 2 }, a_{n+1}=\frac{ 4n-1 }{ 3n+2 }a_n$$
(a) Determine: $$S_2 = a_1 + a_2$$


(b) Determine convergence, divergence of $$\sum_{?}^{?} a_n $$ by the ratio test

loser66 · Answer

can you tell me if a_(n+1 ) = a_2 so, n=?

anonymous · Answer

i dont get it.. problem is just like that.. i don't know how to start.

loser66 · Answer

I am walking you through, so , just answer my question. At the end up, you can understand.

anonymous · Answer

n=2?

anonymous · Answer

wait no n=1

loser66 · Answer

n+1 =2 , how n=2? If n =2 so n+1 =3 , right? try again, tell me if n+1 =2 so n=?

anonymous · Answer

yea it's 1

loser66 · Answer

ok, so with $$a_{n+1}=\frac{4n-1}{3n+2}a_n$$ you replace n =1 at any place you see the letter n. what do you get?

anonymous · Answer

a_2 = 3/5 a_1

anonymous · Answer

$$a_2 = \frac{ 3 }{ 5 } a_1$$

loser66 · Answer

ok, you have a_1 = 1/2 replace to a_2 what do you have ?

anonymous · Answer

$$S_2=a_1+a_2 :\frac{ 1 }{ 2 }+\frac{ 3 }{ 5 }\frac{ 1 }{ 2 } =\frac{ 4 }{ 5 }= S_2 $$

loser66 · Answer

you got it!!! now tell me something about ratio test, what do you know about that?

anonymous · Answer

$$\lim n->\infty : \frac{ \left| A_(n+1) \right| }{ \left| An \right| } =L$$

loser66 · Answer

ok, stop there.

anonymous · Answer

i'm just wondering how do i make that sequence as ∑  ??

loser66 · Answer

from yours, you have, a_(n+1 ) =.... a_n so
a_n+1 /a_n = ....
and then lim (LHS ) = lim RHS. just take lim of RHS and consider whether it converge or diverge, if it converges,  converges to where? that's it

loser66 · Answer

got what I mean?

anonymous · Answer

a liitle bit confused..

anonymous · Answer

what's left hand sum and right hand sum?

anonymous · Answer

a_n+1 will be left hand sum right?

anonymous · Answer

it converges to -1 right? it's my answer

loser66 · Answer

$$a_{n+1}=\frac{4n-1}{3n+2}a_n$$---> $$\frac{a_{n+1}}{a_n}=\frac{4n+1}{3n+2}$$
take limit both sides you have

loser66 · Answer

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