- #1
vin300
- 603
- 4
I have recently discovered some mathematical rules by trial and error. Some of these may be already known to people of mathematics.
1. This one is common: Sum of all integers 1+2+3+...=0.5(n^2 + n)
2. Sum of odd integers: 1+3+5+7+9...= n^2
3. Sum of even integers: 2+4+6+8...= n^2 + n eg: Sum of first two: 2+4= 2^2 +2 =6
4. Sum of gap odd integers(odd integers with one gap) : 1+5+9+13+17...= (n+1)(n+2) eg. 1+5=(1+1)(1+2)=6
5.a. Sum of gap even integers: 2+6+10+14...= 2n^2 eg 2+6+10= 2(3)^2=18
5.b. Sum of gap even integers: 4+8+12+16...= 4(1+2+3+4+...) eg:4+8+12= 4(1+2+3)= 24
1. This one is common: Sum of all integers 1+2+3+...=0.5(n^2 + n)
2. Sum of odd integers: 1+3+5+7+9...= n^2
3. Sum of even integers: 2+4+6+8...= n^2 + n eg: Sum of first two: 2+4= 2^2 +2 =6
4. Sum of gap odd integers(odd integers with one gap) : 1+5+9+13+17...= (n+1)(n+2) eg. 1+5=(1+1)(1+2)=6
5.a. Sum of gap even integers: 2+6+10+14...= 2n^2 eg 2+6+10= 2(3)^2=18
5.b. Sum of gap even integers: 4+8+12+16...= 4(1+2+3+4+...) eg:4+8+12= 4(1+2+3)= 24