Sequences Problem
Given Sa = 2m + (2m+1) + (2m+2) + ... + 4m
and Sb = (2m+1) + (2m+3) + (2m+5) + ... + (4m-1)

If Sa/Sb = k + 1/L , find the values of k and L.

Thank you for the solution.

Question

Sequences Problem
Given Sa = 2m + (2m+1) + (2m+2) + ... + 4m
and Sb = (2m+1) + (2m+3) + (2m+5) + ... + (4m-1)

If Sa/Sb = k + 1/L , find the values of k and L.

Thank you for the solution.

anonymous · Answer

lol everyone left

phantom · Answer

Sa= 6(m^2) + 3(m)
Sb= 3(m^2)
Sa/Sb = 3+ (1/m) so k=3 l=m
How did I get here ???
For Sa: use the fact that 1+2+3+...+n=n(n+1)/2 and Sa=(1+2+3+...+4m)-(1+2+..+2m-1)
to get Sa
For Sb: use the fact that 1+3+5+...+(2n-1)= n^2 and Sb= (1+3+5+...+4m-1)-(1+3+5...+2m-1)= (2m)^2-(m)^2