Strategies for Solving Complex Addition Problems

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Homework Help Overview

The discussion revolves around strategies for solving complex addition problems involving rationalizing fractions and analyzing arithmetic structures. The original poster presents a sequence of terms that includes square roots and seeks methods for simplification or resolution.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss rationalizing fractions and the arithmetic structure of a series involving square roots. Questions arise regarding the validity of certain mathematical expressions and the search for effective methods to approach the problem.

Discussion Status

The conversation includes attempts to clarify mathematical relationships and expressions. Some participants provide feedback on specific calculations, suggesting a need for reevaluation of assumptions. There is an ongoing exploration of the problem without a clear consensus or resolution yet.

Contextual Notes

Participants are navigating potential misunderstandings regarding mathematical identities and the implications of their calculations. The original poster expresses uncertainty about the methods available for solving the problem.

Helly123
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Homework Statement


30db2tc.png


Homework Equations

The Attempt at a Solution


I tried to rationalize the fractions by multiplied it by $$\sqrt{n + 1} - \sqrt{n} $$
it will be sum of $$ \frac {\sqrt{n + 1} - \sqrt{n}} {2n +1} $$

also tried to see the arithmetic structure
$$ 1 + \frac{1}{\sqrt{2} + \sqrt{1}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{1}{\sqrt{4} + \sqrt{3}} ... \frac{1}{\sqrt{121} + \sqrt{120}} $$

is there any method to solve it? that I don't know
 

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Helly123 said:

Homework Statement


View attachment 218012

Homework Equations

The Attempt at a Solution


I tried to rationalize the fractions by multiplied it by $$\sqrt{n + 1} - \sqrt{n} $$
it will be sum of $$ \frac {\sqrt{n + 1} - \sqrt{n}} {2n +1} $$

also tried to see the arithmetic structure
$$ 1 + \frac{1}{\sqrt{2} + \sqrt{1}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{1}{\sqrt{4} + \sqrt{3}} ... \frac{1}{\sqrt{121} + \sqrt{120}} $$

is there any method to solve it? that I don't know

##2n+1## is not equal to the product of ##\sqrt{n + 1} - \sqrt{n}## and ##\sqrt{n + 1} + \sqrt{n}##. Fix that up and then think about it again.
 
Dick said:
##2n+1## is not equal to the product of ##\sqrt{n + 1} - \sqrt{n}## and ##\sqrt{n + 1} + \sqrt{n}##. Fix that up and then think about it again.
thank you...
 
Helly123 said:
thank you...
So ...
What did you get for a result ?
 
SammyS said:
So ...
What did you get for a result ?
11 :)
 

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