The first 2 terms of a geometric progression are 3 and -2. Write
down a simplified expression for the sum to n terms and
evaluate the sum to infinity of this progression.
Find the least value of n for the sum to n terms to be
within 2% of the sum to infinity.
In this case, I shall denote the sum to infinity as 'i' and the
sum to n terms as 'S'
From my understanding, I'd interpret the last statement of the
question as
| S | </= 0.02 i, since the question specifies that it be
within 2%, meaning if the 'S' is 2% of i, it if still valid.
However, the solutions provided gave something like
| S - i | < 0.02 i
and they solved accordingly, getting n = 10 as the answer. If I
used my own method I get n = 7. I wonder why they subtract 'i' from
'S'. And why is the difference LESS than 0.02i and not LESS THAN
OR EQUAL TO 0.02i?
Thank you.
|
http://www.thefreedictionary.com/within
"within" means inside.
I don't think any Maths explanation is needed here, so here
goes:
Imagine a city with a fence around it .
< means inside the city
= means on the fence
> means outside the city
Within is inside, so it does not include being on the fence.
I hope this analogy helps.