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Find the value of
11+12+11+12+

 Jan 18, 2021
 #1
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First, set this equal to x:

x=11+12+11+12+...

We can replace the bottom part with x, shown below:

x=11+12+x

Now, solve for x:

x=12+x+12+xx=13+x2+xx=2+x3+xx2+3x=2+xx2+2x2=0

After using the quadratic formula or completing the square, we find that x=13 or x=31. Since x must be positive, the negative solution is extraneous, and therefore the answer is 31

 Jan 18, 2021

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