anonymous
  • anonymous
sigma
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
What?
anonymous
  • anonymous
\[\sum_{k=1}^{49}(k+1)^3-k^3\] evaluate
anonymous
  • anonymous
no formular jus a series

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anonymous
  • anonymous
That series is just saying when you plug in k = 1, 2, 3, 4....49 and add them up, there should be a formula for the series to make the calculation easier. It is possible to calculate every term.
anonymous
  • anonymous
\[2^3-1^3+3^3-2^3+4^3-3^3+...+50^3-49^3\]
TuringTest
  • TuringTest
it appears to be a telescoping series
anonymous
  • anonymous
does it mean numbers are cancelling out
anonymous
  • anonymous
i think the anwers is \[-1^3+50^3\]
amistre64
  • amistre64
\[\sum_{k=1}^{49}(k+1)^3-k^3\] \[\sum_{k=1}^{49}(k+1)^3-\sum_{k=1}^{49}k^3\] \[\sum_{k=1+1}^{49+1}(k)^3-\sum_{k=1}^{49}k^3\] \[\sum_{k=2}^{50}k^3-\sum_{k=1}^{49}k^3=50^3-1^3\]

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