An easy method?

Question

An easy method?

1 Answer

Impact of this question

1446 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-21T02:22:44

Hint: $\frac{1}{\sqrt{n} + \sqrt{n + 1}} = what$ $1/(sqrtn+sqrt(n+1)) = "what"$ ?

Explanation:

Rationalize the denominators:

$\frac{1}{(\sqrt{n} + \sqrt{n + 1})} \cdot \frac{(\sqrt{n} - \sqrt{n + 1})}{(\sqrt{n} - \sqrt{n + 1})} = \frac{\sqrt{n} - \sqrt{n + 1}}{n - (n + 1)}$ $1/((sqrtn+sqrt(n+1))) * ((sqrtn - sqrt(n+1)))/((sqrtn-sqrt(n+1))) = (sqrtn-sqrt(n+1))/(n-(n+1))$

$= \sqrt{n + 1} - \sqrt{n}$ $= sqrt(n+1)-sqrtn$

So the sum above is equivalent to

$(\sqrt{2} - 1) + (\sqrt{3} - \sqrt{2}) + (\sqrt{4} - \sqrt{3}) + \cdot \cdot \cdot + (\sqrt{8} - \sqrt{7}) + (\sqrt{9} - \sqrt{8})$ $(sqrt2 - 1) + (sqrt3 - sqrt2) +(sqrt4-sqrt3) + * * * +(sqrt8-sqrt7) + (sqrt9 - sqrt 8)$
Which is $- 1 + \sqrt{9} = 2$ $-1+sqrt9 = 2$

Science

Math

Humanities

... and beyond

An easy method?

1 Answer

Explanation:

Related questions

Impact of this question