Sequences

Jul 2008
212
2
This sequence is defined implicitly. List the first six terms of this sequence.

a0 = 1 and an+1 = an + (1/(2^n))

The 0 and the an's are suppose to be small and lower to the letters, you know what I mean I hope!
 
Feb 2010
100
27
Lebanon - Beirut
you should simply follow the recurrence given:
\(\displaystyle a_0=1\)
\(\displaystyle a_1=a_0+\frac{1}{2^0}=1+\frac{1}{2^0}=2\)
\(\displaystyle a_2=a_1+\frac{1}{2^1}=2+\frac{1}{2^1}=2.5\)
and so on...

hope this helps
 
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Jul 2008
212
2
Is a0 part of the "six" terms thus I only find the terms for a0 to a5, or do I just find out from a1-a6? It says the "first six terms"....
 
Feb 2010
100
27
Lebanon - Beirut
I think what is meant is the first six terms starting form \(\displaystyle a_0\) since the sequence is defined by \(\displaystyle a_0\) as the first term. Hence you should provide \(\displaystyle a_0\).......\(\displaystyle a_5\)
 
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