Maths is this questions answer below?

Question

Charles Anctil · Accepted Answer

# sum_(n=64)^98 \ (4n^2-5) = 932645 #

Making (b) the correct solution.

We seek: # S = sum_(n=64)^98 \ (4n^2-5) # # S = sum_(n=1)^98 \ (4n^2-5) - sum_(n=1)^63 \ (4n^2-5) # Applying the common summation formulae: # sum_(r=1)^n \ r^2 = 1/6n(n+1)(2n+1) # We have: # sum_(r=1)^n \ (4r^2-5) = 4sum_(r=1)^n r^2 - sum_(r=1)^n 5 # # " " = 2/3 n(n+1)(2n+1) - 5n # # " " = n/3{ 2(n+1)(2n+1) - 15} # # " " = n/3{ 2(2n^2+3n+1) - 15} # # " " = n/3{ 4n^2+6n+2 - 15} # # " " = n/3{ 4n^2+6n-13} # With this outcome, we get: # S_98 = 98/3{ 38416+588-13} # # \ \ \ \ \ = 98/3{ 38991 } # # \ \ \ \ \ = 1273706 # And: # S_63 = 63/3{ 15876 + 378 - 13} # # \ \ \ \ \ = 63/3{ 16241 } # # \ \ \ \ \ = 341061 # So then: # S = S_98 - S_63 # # \ \ = 1273706 - 341061 # # \ \ = 932645 # figuring out the right answer (b).

Emma Aldridge · Answer

undefined It seems there is no specific question provided. Could you please provide the question or clarify what you are asking?