I need to prove by induction on n, that

4^1 + 4^2 + 4^3 +....+ 4^n = 4/3 (4^n) - 1

For all integers 'n' is = or > than 1

Thank you very much!

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- February 27th 2010, 09:04 AMOsbourneOz'Proof' help needed please...
I need to prove by induction on n, that

4^1 + 4^2 + 4^3 +....+ 4^n = 4/3 (4^n) - 1

For all integers 'n' is = or > than 1

Thank you very much! - February 27th 2010, 09:22 AMchisigma
The sum of the first n terms of a 'geometric progression' is...

(1)

Setting in (1) what do You obtain?...

Kind regards

- February 27th 2010, 10:33 AMOsbourneOz
Sorry, but I am totally lost!

Oz - February 27th 2010, 10:50 AMchisigma
Taking into account the identity...

(1)

... you arrive to demostrate that is...

(2)

... so that...

Kind regards

- February 27th 2010, 12:39 PMLaurent
In a proof by induction, you have to

a) check the initial case: here, you have to check the identity when .

b) perform the induction step: assume that, for some , ; then you have to prove that (same identity with instead of ). To do this, simply note that (using the assumption), and after simplification you should get what you need. This will conclude the induction.