anonymous one year ago Need help. Will medal and fan

1. anonymous

$\frac{ 1 }{ 2 }+\frac{ 1 }{ 3 }+...+\frac{ 1 }{ x }>1 \frac{ 1 }{ 2 }$

2. anonymous

What is the smallest posible value of x

3. anonymous

X=1

4. SolomonZelman

$\large \sum_{n=2}^{x}\frac{ 1 }{ n }>1+\frac{ 1 }{ 2 }$ this is the problem (i am kinda slow right now esp. with foreign keyboard)

5. SolomonZelman

$$\displaystyle\large \sum_{n=2}^{x}\frac{ 1 }{ n }>1+\frac{ 1 }{ 2 }$$ $$\displaystyle\large \sum_{n=3}^{x}\frac{ 1 }{ n }>1$$

6. SolomonZelman

i am thinking about it sorry...:)

7. SolomonZelman

do partial sums suffice or want some legit math? because so far i only see partial sums

8. anonymous

Do whatever you can

9. SolomonZelman

1/3+1/4=7/12 7/12 + 1/5 = (35+12)/60 = 47/60 47/60 + 1/6 = (47 + 10)/60 = 57/60 57/60 + 1/7 = (399 + 60)/420 = 459/420

10. SolomonZelman

$$\displaystyle\large \sum_{n=3}^{x}\frac{ 1 }{ n }>1$$ $$\displaystyle\large x=7$$ based on partial sums

11. anonymous

yay!