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Find 1 + 1/2 + 1/6 + 1/12 + 1/36+...., where we alternately multiply by 1/2 and 1/3 to get the next term.

 Feb 27, 2022
 #1
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Separate this into two geometric sequences.

 

(1 + 1/6 + 1/36 + ...) + (1/2 + 1/12 + ...)

= 1/(1 - 1/6) + (1/2)/(1 - 1/6)

= 6/5 + (1/2)*(6/5)

9/5

 Feb 27, 2022

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