anonymous
  • anonymous
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.
Mathematics
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anonymous
  • anonymous
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.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
lol everyone left
phantom
  • phantom
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

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