1.S even -S odd =nd
S odd /S even =S odd /(S odd +nd)=(S odd +nd-nd)/(S odd +nd)= 1-nd/(S odd +nd)
S odd number =na 1+n(n- 1)*2d/2 (odd column tolerance is 2)=na 1+n2d-nd.
S odd number +nd=na 1+n2d
Nd/(S odd number +nd)=d/(a 1+nd)
2.S odd /S even = 1-nd/(S odd+nd) = (a1+(n-1) d)/(a1+nd) = an/an+/kloc-0.
When the number of terms is 2n+ 1, the middle term is n+ 1.
3.S odd -S even =a 1+nd=an+ 1=a medium.
S odd /S even =(S even+one middle) /S even = 1+ one middle /S even.
A in =(a2+a2n)/2
S even =n(a2+a2n)/2(2n+ 1 column has n even numbers, n+ 1 odd numbers, and the sum of even numbers is n/2 a2+a2n).
4. So s odd /S even =(S even +a middle) /S even = 1+a middle /S even =1+1/n = (n+1)/n.
When the number of terms is 2n- 1, the middle term is n.
5.S odd -S even =a 1+(n- 1)d=an=a medium.
6. Similarly, it is proved that S odd /S even =(S even +a middle) /S even = 1+a middle /S even =1(n-1) = n/(n-1).