# Proof by induction

I need help to solve this problem

Use induction to prove that, for n>=0:

3*5^0 + 3*5^1 + 3*5^2 + 3*5^3 + ...+ 3*5^n = 3*(5^(n+1)-1)/4

in other word

n

$$\sum$$ 3*5 k= 3*(5 n+1-1) / 4
k= 0

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rock.freak667
Homework Helper
Assume true for n=N and now prove true for n=N+1.
Do you know how to do a proof by induction?

I did these steps and I tried to complete the rest but I don't know some of the steps

and what I is in the attached doc.

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rock.freak667
Homework Helper
Try not to upload word documents as these usually contain viruses. Can you type out the steps you did?

Basis: n= 0
0
$$\sum$$3*5^ 0 = 3

k= 0

3*(5 0+1-1) / 4 = 3

Assume:

n

$$\sum$$ 3*5^k= 3*(5 n+1-1) / 4
k= 0

Prove:

n+1

$$\sum$$ 3*5 ^k= 3*(5 (n+1)-1) / 4
k= 0

________________________________________
Proof:

n+1
$$\sum$$ 3*5^ k =

k= 0

As you have the base case, think about the sum:

3*5^0 + 3*5^1 + 3*5^2 + 3*5^3 + ...+ 3*5^n + 3*5^(n+1)

which is now your inductive step, as rock.freak667 suggested.

What are the two ways in which this can also be written with the information you already have?

The Bob