SOLUTION: Simplify: 1+(1/(1+(1/(1+(1/(1+(1/x))))))) if that makes no sense, it's also written something like (ignore the periods): 1+ ________1________ .......1+ ______1______ ...

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify: 1+(1/(1+(1/(1+(1/(1+(1/x))))))) if that makes no sense, it's also written something like (ignore the periods): 1+ ________1________ .......1+ ______1______ ...      Log On


   

Question 62894This question is from textbook Algebra and Trigonometry
: Simplify:
1+(1/(1+(1/(1+(1/(1+(1/x)))))))
if that makes no sense, it's also written something like (ignore the periods):
1+ ________1________
.......1+ ______1______
..............1+ ____1____
......................1+ (1/x)
Thank you so much! This question is from textbook Algebra and Trigonometry

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
LET Y = 1+(1/(1+(1/(1+(1/(1+(1/x)))))))
IS IT TO INFINITE TERMS? IF SO,WE CAN SAY THAT
Y = 1+ 1/Y AS THE NUMBER OF TERMS ARE UP TO INFINITY
Y^2-Y-1=0
Y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Y+=+%281+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
Y+=+%281+%2B+sqrt%28+5+%29%29%2F%282%29+

if that makes no sense, it's also written something like (ignore the periods):
1+ ________1________
.......1+ ______1______
..............1+ ____1____
......................1+ (1/x)