This theory may help you........................................................(You may decide what you want to add here)
n=0 0²=0
n=1 1²=1
n=2 2²=1+3=4
n=3 3²=1+3+5=9
n=4 4²=1+3+5+7=16
n=5 5²=1+3+5+7+9=25
n=6 6²=1+3+5+7+9+11=36
n=7 7²=1+3+5+7+9+11+13=49
n=8 8²=1+3+5+7+9+11+13+15=64
n=9 9²=1+3+5+7+9+11+13+15+17=81
n=10 10²=1+3+5+7+9+11+13+15+17+19=100
On that given pattern/sequence we can create a new THEORY
THEORY 1.1
"The sum of all consecutive odd numbers,starting from one,are perfect square"
And under of my obervation,the number of consecutive odd number/s is equivalent to n.And the highest on given odd numers is always equals to (2n-1)
Therefore,
If n=54(for example)
25²=1Σ(2n-1);All odd numbers
or
25²=1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37+39+41+43+45+47+49------->Lets check if Im right...
2n-1=49;n=25
2(25)-1=49?
50-1=49
49=49
Therefore this theory have now a proof.And let see if the number of odd numbers are 25.
(Count the equation and I think Im right)
Therefore thats theory have a proof too.
But if n is not given,and the problem/equation is,
1(if its starting from 1)Σ37;all odd numbers
to find it out we can use the formula:[½(L+1)]²;L=the largest odd number
SO
[½(37+1)]²=?
[½(38)]²=?
(19)²=361
So the equaion is true and n=19
So n=(L+1)/2
Therefore as general,
n²=(n-1)²+(2n-1)
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My Mathematical Theories
RandomPara sa akin lang ito! nasa sa inyo kung gusto niyong magdugo ang mga utak niyo. Conjectures, Problems, Hypothesis.
