# integral testWatch

#1
http://plus.maths.org.uk/issue19/fea...ndex-gifd.html

i don't understand how part of equation (15) comes about. how come 1 + ln(n) < (the sum)? isn't the second comparison, which isn't written down:

sum < ∫(1/x)dx
sum < ln(x)

where does the one come from???

using ln(x), we get ln(x+1) < sum < ln(x) which can't even be possible...
0
quote
13 years ago
#2
it's because lnx has the y axis as an asymptote so rather than saying that the sum is less than the integral for all of it, you know that the first number in the sum is 1 and so you use that instead. that doesnt come accross very clearly in my explanation.

the one is basically just adding on the first bit of the sum, the rectangle of area 1 because otherwise the integral is messy. i think thats what youre asking.
0
quote
#3
ah ha. thankyou.
0
quote
13 years ago
#4
you appear to have understood, but i just realised, its nothing to do with y=lnx being an asymptote, its y=1/x. and is it me or is the label under the graph under equation (15) wrong, it is 1/n underneath 1/x isn't it . . . not 1/1+x. minor detail.
0
quote
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• University of Buckingham
Fri, 14 Dec '18
• University of Lincoln
Mini Open Day at the Brayford Campus Undergraduate
Wed, 19 Dec '18
• University of East Anglia
Fri, 4 Jan '19

### Poll

Join the discussion

Yes (91)
25.93%
No (260)
74.07%