The Student Room Group
ShortRef
from a book:

What does he mean by 'check' this result? By calculation? (this book is from the 1940's).


I guess so - the only two meanings I can see are "you should check it (so you understand how it works and are happy)" and "you should check it (because I might be wrong)". I can't see it being the latter! :p:
I wonder why e is rounded when it is easier to remember it as 2.718281828

Although it has 18181828, e is not a recurring decimal. (The reader should check *this* result)
Reply 3
You can also put bounds on the error between the partial sum and e. For example, if I recall correctly,

e - 1 - 1 - 1/2! - ... - 1/n! < 1/(n x n!).
Reply 4
I would think the expectation is that you will check that the sum does actually come to that value (and in the process get an appreciation for how quickly the series converges).
Reply 5
DFranklin
I would think the expectation is that you will check that the sum does actually come to that value (and in the process get an appreciation for how quickly the series converges).


I think Shortref was wondering whether a (typical) reader would be able to do this in the 1940s.

I'm getting
1+
1+
0.5+
0.1666....+
0.041666666.....+
that decimal divided by 5 +
that decimal divided by 6 etc..

A bit of a pain but not difficult.

I think the answer is yes depending on who the book was aimed at.
Reply 6
Yes, it's not at all difficult. (Difficult without pen and paper, but well within the abilities of an bright schoolboy with a notepad).
Reply 7
DFranklin
Yes, it's not at all difficult. (Difficult without pen and paper, but well within the abilities of an bright schoolboy with a notepad).


or girl..:wink:
Reply 8
rnd
or girl..:wink:


or Mother. :wink:
Reply 9
*MJ*
or Mother. :wink:

Whatever thread I look at, you've posted a reply!
Reply 10
Bezzler
Whatever thread I look at, you've posted a reply!


It's called being a TSR legend. :cool:
DFranklin
Yes, it's not at all difficult. (Difficult without pen and paper, but well within the abilities of an bright schoolboy with a notepad).


Or schoolgirl....

People were taught how to calculate BC (Before Calculators) We were taught how to calculate square roots in my primary school. That is a waste of time when you can now just press a button.
rnd
I think Shortref was wondering whether a (typical) reader would be able to do this in the 1940s.

I'm getting
1+
1+
0.5+
0.1666....+
0.041666666.....+
that decimal divided by 5 +
that decimal divided by 6 etc..

A bit of a pain but not difficult.

I think the answer is yes depending on who the book was aimed at.


That was how to calculate e to the something on early calculators.
Reply 13
I suppose its not hard just using long division, tedious is a better word :smile:

I'm not going to do it though. A few months ago I wrote a program to approximate e this way, it does converge very quickly.
*MJ*
It's called being a TSR legend. :cool:

you're not though.

me on the otherhand.

Latest