Find the number of terms in the following geometric series: 1 + 2 + 4 + ... + 67108864
Answer & Explanation
The general form of a term of a geometric sequence or series is:
where a is the first term and r is the common ratio.
In our example, a=1 and r=2, so the question boils down to identifying which power of 2 is 67108864.
Notice that and 67108864 is a little over hence we find the correct power is:
So there are 27 terms:
As a child, I used to like to write powers of 2 on a blackboard, starting with 1 and doubling it repeatedly.
In later life I found it useful to memorise powers of 2 up to about
A couple of 'fun' ones are and (which contains all the digits except 4).
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