adding fractions

[renegade05]

[attachment=066pmli4]Capture.JPG[/attachment66pmli4]

Alright, I know this is probably super easy, but how do you do this?

I am stuck.

And yes of course this is on a no-calculator portion of an exam - and I am guessing there is a series i need to evaluate.

 

[galactus]

I presume this is a practice exam?.

Break up each term:

\(\displaystyle \left(\underbrace{1-\frac{1}{2}}_{\text{1/2}}\right)+\left(\underbrace{\frac{1}{2}-\frac{1}{3}}_{\text{1/6}}\right)+\left(\underbrace{\frac{1}{3}-\frac{1}{4}}_{\text{1/12}}\right)+\cdot\cdot\cdot +\left(\frac{1}{k-1}-\frac{1}{k}\right)+\left(\frac{1}{k}-\frac{1}{k+1}\right)\)

See?. It telescopes.