The 35 years ago
1 9 8 1 + 1 9 8 1 − 1 9 8 1 + 1 9 8 1 − 1 9 8 1 + ⋯ = ?
The answer is 45.
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1 solution
I keep asking this question: How do you know that it converges?
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And its highly probable that you will not get a answer here too :-)
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Why don't you defy the odds?
Or, better yet, prove the convergence of this one . Good luck with that! ;)
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@Otto Bretscher – Oh... Need to study for that.... Convergence is something which I came to know on briliant and I really need to work on that concept real hard... And still this question can be approached by:
x = 1 9 8 1 + 1 9 8 1 − 1 9 8 1 + 1 9 8 1 − ⋯ = 1 9 8 1 + y y = 1 9 8 1 − 1 9 8 1 + 1 9 8 1 − 1 9 8 1 + ⋯ = 1 9 8 1 − x Then squaring , manipulating and subtracting will do the job but I knew I would end up having convergence issues.. :-)
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@Rishabh Jain – We can consider the iteration function f ( x ) = 1 9 8 1 + 1 9 8 1 − x with the seed a 0 = 1 9 8 1 ≈ 4 4 . 5 . This is a very strong contraction, with ∣ f ′ ( x ) ∣ < 0 . 0 0 1 on [ 4 4 , 4 6 ] , so that the nested radical will converge to 45 very quickly.
@Rishabh Jain – The best way!!!
Let
be A. If we square A. We get 1981 +
. However,
is also A. Hence A^2 = 1981 + (1981-A)^(1/2), A=45.