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Verify and prove (Posted on 2017-12-10) Difficulty: 4 of 5
Consider:
      (15 + 25)     +     (17 + 27)     =   2 *(1 + 2)4   
   (15 + 25 + 35)   +   (17 + 27 + 37)   =  2 *(1 + 2 + 3)4 
(15 + 25 + 35 + 45) + (17 + 27 + 37 + 47) = 2 *(1 + 2 + 3 + 4)4
       ...                  ...       and so on     ...

First, verify that both sides are equal for further increase in n,

then prove it.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts computer verification no proof | Comment 1 of 5
n   LHS    RHS

2   162    162
3   2592    2592
4   20000    20000
5   101250    101250
6   388962    388962
7   1229312    1229312
8   3359232    3359232
9   8201250    8201250
10   18301250    18301250
11   37949472    37949472
12   74030112    74030112
13   137149922    137149922
14   243101250    243101250
15   414720000    414720000
16   684204032    684204032
17   1095962562    1095962562
18   1710072162    1710072162
19   2606420000    2606420000
20   3889620000    3889620000
21   5694792642    5694792642
22   8194304162    8194304162
23   11605565952    11605565952
24   16200000000    16200000000
25   22313281250    22313281250

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 lhs1 = Int(1 + 2 ^ 5 + 0.5)
 lhs2 = Int(1 + 2 ^ 7 + 0.5)
 rhsTot = 3
 
 For nxt = 3 To 26
   Text1.Text = Text1.Text & nxt - 1 & "   "
   Text1.Text = Text1.Text & lhs1 + lhs2 & "    " & 2 * rhsTot * rhsTot * rhsTot * rhsTot & crlf
   lhs1 = lhs1 + nxt * nxt * nxt * nxt * nxt
   lhs2 = lhs2 + nxt * nxt * nxt * nxt * nxt * nxt * nxt
   rhsTot = rhsTot + nxt
   DoEvents
 Next
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2017-12-10 10:26:50
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