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Question no. 10,Observing that 1^3=1,2^3=3+5,3^3=7+9+114^3=13+15+17+19,find a general formula for the cube of natural no. n

Question no. 10,Observing that 1^3=1,2^3=3+5,3^3=7+9+114^3=13+15+17+19,find a general formula for the cube of natural no. n

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Grade:12th pass

1 Answers

Md Shaquib Ansari
13 Points
5 years ago
If n=odd then,n3=
  \sum_{-(n-1)/2}^{(n-1)/2} (n^{2}+2r)
If n= even then, n3=
\sum_{-(n/2)+1}^{(n)/2} (n^{2}+2r-1)
You can observe the pattern given in the question and you will see that middle value of the series is either n2 or n2 -1 depending on whether n is odd or even.Rest is just simple arrangement of terms.

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