Evaluate -1/3-2/3^2-2^2/3^3-2^4/3^4-2^7/3^5+2^11/3^5 w/o calculator

[dellboy1234]

evaluate

-1/3-2/3^2-2^2/3^3-2^4/3^4-2^7/3^5+2^11/3^5

without using a calculator,

Thanks for your help!!

 

[Deleted member 4993]

evaluate

-1/3 - 2/3^2 - 2^2/3^3 - 2^4/3^4 - 2^7/3^5 + 2^11/3^5

without using a calculator,

Thanks for your help!!

Please confirm that the operation indicated in red is correct.

 

[ksdhart]

You have six fractions you're adding and subtracting. As you surely know, to add or subtract fractions you need to find a common denominator for all of them. So, what do you think the common denominator is for this problem?

\(\displaystyle \displaystyle -\frac{1}{3}-\frac{2}{3^2}-\frac{2^2}{3^3}-\frac{2^4}{3^4}-\frac{2^7}{3^5}+\frac{2^{11}}{3^5}\)

When all the fractions have a common denominator and you add/subtract, what do you get? Can you simplify that result at all?

 

[Ishuda]

evaluate

-1/3-2/3^2-2^2/3^3-2^4/3^4-2^7/3^5+2^11/3^5

without using a calculator,

Thanks for your help!!

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting


Hint: The first three terms are geometric, i.e.
-1/3 - 2/3² - 2²/3³ = -(1/3) [ 1 + x + x²] = -(1/3) [1 - x³] / [1 - (2/3)]
where x=2/3. Now turn the rest of the terms into something*x and you should be able to add them up fairly easily.