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Summing Exponents

Date: 06/11/2002 at 16:57:23
From: Matt
Subject: sequences

A student multiplies successive powers of 3,

  3^1  * 3^2 * 3^3 * ...

gets an answer of 3^210.  Find the last power of 3 in the list.

I don't even know where to start.  Is it a geometric series?

Date: 06/11/2002 at 18:08:32
From: Doctor Ian
Subject: Re: sequences

Hi Matt,

If you're not comfortable yet with the properties of exponents, 
you might want to look at 

  Properties of Exponents 

before reading further. 

Okay, now note that 

    3^1 * 3^2 * 3^3 * ... * 3^n

  = 3^(1 + 2 + 3 + ... + n)

  = 3^210

So the question is really asking you how many integers you have 
to add up to get a sum of 210. 

Can you take it from here?

- Doctor Ian, The Math Forum 
Associated Topics:
High School Exponents
High School Sequences, Series

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