pretty bad at AP and GP (1 Viewer)

[DarkDude]

The sum to 'n' terms of a certain series is 2^n+1 - 2. Prove that the nth term is given by 2^n+1 - 2^n.

I tried solving this by writing 2^n+1 - 2 in the form of ar^n - a/r-1 and i got stuck is there a better way?

 

[Jago]

S_n - S_n-1 = T_n

that's how i would do it if it weren't so hot.

Edit: maybe not... :/

 

[sikeveo]

dreamerish got it wrong.

 

[acmilan]

Is it an arithmetic or geometric series?

 

[DarkDude]

i still cant figure it out

 

[DarkDude]

i think its geometric, but it doesnt say

 

[rama_v]

The sum to 'n' terms of a certain series is 2^n+1 - 2. Prove that the nth term is given by 2^n+1 - 2^n.

I tried solving this by writing 2^n+1 - 2 in the form of ar^n - a/r-1 and i got stuck is there a better way?

You can prove it by induction, but thats 3 unit. But I guess it might still be valid.
I will skip to the assume true for n=k step:

2^k+1 - 2^k = 2^k+1 -2

Need to prove true for n = k+1
i.e. prove:
2^k+1 - 2 + 2^k+2 - 2^k+1 = 2^k+2 - 2
LHS = 2^k+1(1+2-1) -2
= 2^k+1(2) -2
= 2^k+2 - 2
= RHS
therefore proven true for n=k+1 blah blah, english has drained all the energy out of me lol

 

[DarkDude]

wow!that looks complicated. thanks a lot rama.

 

[rama_v]

S_n - S_n-1 = T_n

that's how i would do it if it weren't so hot.

Edit: maybe not... :/

hey lol that method works
just got to simplify what they've given you
(2ⁿ⁺¹ - 2) - (2ⁿ - 2)
= 2ⁿ⁺¹ - 2 - 2ⁿ + 2
= 2ⁿ(2-1)
= 2ⁿ

RHS =

2ⁿ⁺¹ - 2ⁿ
= 2ⁿ(2 - 1)
= 2ⁿ
= LHS as required

 

[Jago]

oh damn, why didn't i simplify RHS

 

[MarsBarz]

Well to find out if it's an arithmetic serie or a geometric serie what you could do with this question is cheat and test 3 consecutive numbers (for n) in the answer they gave us in the actual question ( T_n = 2^n+1 - 2^n ).

 

[Meldrum]

dreamerish got it wrong.

HAHAHAHAHA, and she accordingly deleted her post.

Can't allow people to know about miss perfection's mistake.