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Babna J.

asked • 02/10/14

Determine the 2010th term for the following sequence: 1,2,3,6,7,14,15,30,31,62,63

I need the steps used to figure out the equation.

4 Answers By Expert Tutors

By:

Kenneth G. answered • 02/10/14

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New to Wyzant

Experienced Tutor of Mathematics and Statistics

Ryan S.

Wolframalpha will do it. http://www.wolframalpha.com/input/?i=2%5E1006-2
685765508599211085406992031398401158759299079491541508764000248557024672719959118395646962442045349201660590667234013968119772982843080987903012964780708787451812337588750783066948774723991753080189067657794974398949244241113521123786594812548932026532556574571938698730267509225767960757581162756440062
But I haven't verified the accuracy.
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02/10/14

Kenneth G.

Thanks Ryan!   I forgot about trying Wolfram.
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02/10/14

James A.

Machine precision in nowhere near that good. Anything after to 20th value is almost definitely going to be meaningless
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02/10/14

Ryan S.

Again, I haven't personally verified the result, but I would not dismiss it out of hand. There are peer-reviewed published values of numbers such as pi computed to a million digits or more. Algorithms can be developed that do not rely merely on the accuracy of floating point operations.
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02/10/14

James A.

that is true.  I guess wolfram alpha could define a data type with an arbitrary bit length to get any precision needed.  Not sure if that is done or not, but would be interesting to know
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02/10/14

Kenneth G.

The number has 303 digits, the correct number.  I would bet that it's correct.  I've found some errors on Wolfram before, but they generally have been minor.
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02/10/14

Ryan S.

It is interesting to note that Wolfram's result for 2^1006 ends in the digits 64 which is 2 more than the last two digits of the result for (2^1006)-2. (62)
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02/10/14

Kenneth G.

First of all, 1006 - 2 = 1004, and 1004/4 = 251.  This is significant because it means 21006 ends in the digit 4, which means 21006 - 2 ends in the digit 2.  So I claim that the Wolfram answer ends in the correct digit.
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02/10/14

Kenneth G.

Note that the number 21006 = 21004 *24,  and 1004/4 = 251.   This means that 21006 ends in the digit 4, which means that the Wolfram answer ends with the correct digit.
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02/10/14

Ryan S. answered • 02/10/14

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4.8 (10)

Mathematics and Statistics

James A.

Haha nice, I personally wouldn't trust any computer calculation out past ~20 digits, and there are very few applications that actually require that level of precision.  I believe they calculate pi out to thousands of digits one at a time, therefore not ever needing to store the entire number out to full precision.
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02/10/14

James A. answered • 02/10/14

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New to Wyzant

I teach how to understand the math, rather than how to do it

Steve S. answered • 02/10/14

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5 (3)

Tutoring in Precalculus, Trig, and Differential Calculus

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