How do you use the properties of summation to evaluate the sum of #Sigma (i-1)^2# from i=1 to 20?
1 Answer
Dec 20, 2016
# = sum_(i=1)^20 i^2+sum_(i=1)^20 (-2i)+sum_(i=1)^20 1#
# = sum_(i=1)^20 i^2 -2sum_(i=1)^20 i+sum_(i=1)^20 1#
Apply summation formulas to get
# = ((20)(21)(41))/6-2 ((20)(21))/2 + 20#
# = ((10)(7)(41))-2 ((10)(21)) + 20#
# = 2870 - 420 + 20#
# = 2470#
