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.
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
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Posted by Charlie
on 2017-12-10 10:26:50 |
computer verification no proof
