Terms for Reaching 10^57 in a Series?

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Discussion Overview

The discussion centers around determining how many terms are needed in a specific series to approach the value of 10^57. The series in question is defined as 3 + 12 + 27 + 48 + ... and is related to a sum of squares.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant asks how many terms are needed in the series to get close to 10^57.
  • Another participant suggests using the sum of squares formula to calculate the required terms.
  • A different participant proposes that if an error margin of 10^58 is allowed, then only one term is necessary, arguing that 3 is a close approximation to 10^57.
  • A participant expresses gratitude for the assistance provided in the discussion.

Areas of Agreement / Disagreement

The discussion includes differing views on the number of terms needed, with one participant suggesting one term suffices under certain conditions, while another proposes a more traditional approach using the sum of squares formula. No consensus is reached.

Contextual Notes

The discussion does not clarify the assumptions behind the error margin or the specific conditions under which the calculations are made. The dependence on the sum of squares formula is also not fully explored.

kurious
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How many terms would I need in the sum:
3 + 12 + 27 + 48 + ...

( 1x + 4x + 9x +16x + ...)

to get close to the number 10^57 ?
 
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Use the sum of squares formula.

1^2 + 2^2 + ... + n^2 = n (n+1) (2n+1) / 6
 
kurious said:
How many terms would I need in the sum:
3 + 12 + 27 + 48 + ...

( 1x + 4x + 9x +16x + ...)

to get close to the number 10^57 ?

Actually, if you allow an error margin of 10^58, one term is enough!
Since most numbers are larger than 10^58, 3 is a pretty close approximation to 10^57..
 
Thanks for helping.
 

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