What is the sum of all of the perfect squares between #15# and #25#, inclusive, minus the sum of all of the other numbers between #15# and #25,# inclusive?

Question from AoPS
Information
Subject: Pre-Algebra
Focus: Squares

Answer 1

Aurora Arias

#-138#

The only perfect squares between 15 and 25 inclusive are #16 and 25#

#:.# Sum of perfect squares #=16+25 = 41#

The sum of the natural numbers between #17 and 24# is given by:

#S_8 = 8/2(17+24) = 4xx41 =164#

#:.# Sum of the other numbers #=15+164 = 179#

We are asked for the sum of perfect squares minus the sum of the other numbers:

Sum #= 41-179= -138#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

What is the sum of all of the perfect squares between #15# and #25#, inclusive, minus the sum of all of the other numbers between #15# and #25,# inclusive?

Question from AoPS Information Subject: Pre-Algebra Focus: Squares

Question from AoPS
Information
Subject: Pre-Algebra
Focus: Squares