Problem 3: This problem itself is directly creating perceptual curiosity
and at the cognitive level it is against what is known in the
mathematics.
The problem is:
13+23+33+β¦. +n3 = (1+2+3+β¦+n) 2
Visual representation of problem:
Sum of the cubes equal to square?
13+23+33+β¦+ n3 = (1+2+3+β¦+n) 2
+ + +β¦+
=
Direct proof is required. HOWEVER, Proof by Induction IS NOT wanted as
the solutions, that is:
1-For n=1 is true
2- For n = k assumed to be true
6-Show for n = k+1 is true
THIS SOLUTION IS NOT ACCEPTED. WE DONβT WANT THIS SOLUTION
(1+2+3+β¦+n)
n3
23
33
13
Mathematics Homework Solutions
#8920
Working with the sum of cubes.
Please see the attached file for the fully formatted problems.
Problem 3: This problem itself is directly creating perceptual curiosity and at the cognitive level it is against what is known in the mathematics.
The problem is:
13+23+33+
. +n3 = (1+2+3+
+n) 2
Visual representation of problem:
Sum of the cubes equal to square?
13+23+33+
+ n3 = (1+2+3+
+n) 2
+ + +
+ =
Direct proof is required. HOWEVER, Proof by Induction IS NOT wanted as the solutions, that is:
1-For n=1 is true
2- For n = k assumed to be true
6-Show for n = k+1 is true
THIS SOLUTION IS NOT ACCEPTED. WE DON'T WANT THIS SOLUTION
A proof is offered equating a sum fo cubes to an expression of squares.
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