Solving the B Sequence: Tips and Tricks for Finding the Closed-Form Solution

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SUMMARY

The closed-form solution for the sequence B = 1, -1/2, +1/4, -1/8, +1/16, ... is expressed as (-1/2)^n, where n starts from 0. The sequence alternates in sign and halves the absolute value with each subsequent term. The confusion regarding the initial term and the representation of the sequence is clarified by recognizing that both -1/2 and 1/(-2) yield the same value. The mathematical property (a/b)^n = a^n/b^n is also relevant in understanding the manipulation of terms within the sequence.

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mknabster
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This sequence is stumping me, how would I go about solving this?

Write the sequence B = 1, -1/2, +1/4, -1/8, +1/16, ... in closed-form. I tried using (-1) has the top with different variable son the bottom, but nothing seems to add up. The 1 in the front is throwing me off. Any help would be appreciated. thank you
 
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(-1/2)n, where n starts from 0.
 
Oh so you do include 0 in the number line. HOw does this look: 1/(-2)n
 
mknabster said:
Oh so you do include 0 in the number line. HOw does this look: 1/(-2)n
It looks the same. -1/2 = 1/(-2)

Also (a/b)n = an/bn
 

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