Strategies for Solving Complex Addition Problems

In summary, the conversation discusses the attempt at solving a mathematical problem involving rationalizing fractions and finding a method to solve it. The solution involves fixing an error and then reevaluating the problem.
  • #1
Helly123
581
20

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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  • #2
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.
 
  • #3
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...
 
  • #4
Helly123 said:
thank you...
So ...
What did you get for a result ?
 
  • #5
SammyS said:
So ...
What did you get for a result ?
11 :)
 

What is the process for solving an addition problem?

The process for solving an addition problem involves adding the individual digits from right to left, carrying over any excess values to the next column, until all digits have been added.

What is the order of operations for solving an addition problem?

The order of operations for solving an addition problem is to first add any numbers within parentheses, then add or subtract numbers from left to right, and finally multiply or divide numbers from left to right.

What do I do if there are decimal numbers in the addition problem?

If there are decimal numbers in the addition problem, align the decimal points and add the digits as usual, carrying over any excess values to the next column. The final answer should also have a decimal point in the appropriate place.

How do I check if my addition is correct?

To check if your addition is correct, you can use the inverse operation of subtraction. Simply subtract the smaller number from the larger number to see if the result matches the other addend. You can also use a calculator or double check your work by adding the numbers in a different order.

What are some common mistakes to avoid when solving an addition problem?

Some common mistakes to avoid when solving an addition problem include forgetting to carry over excess values, misaligning decimal points, incorrectly adding or subtracting numbers, and mixing up the order of operations. It is important to double check your work and be careful with your calculations.

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