give a formula for finding "a",plz!
2007-02-18 00:09:54 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I am assuming you have to sum to n terms
a = {10-1} + {100-1} + {1000-1}+ ... n terms
a = [10 + 100 + .... n terms ] - [1+1+... n terms]
a = [10 + 100 + .... n terms ] - n
use sum of n terms of a G.P with first term 10 and common ratio 10 for the first expression
2007-02-18 00:17:39 · answer #1 · answered by mth2006to 3 · 0⤊ 0⤋
I assume that you don't mean an infinite series and that your series comes to an end with (10^n) - 1 where n is some finite integer. This gives you the clue as to how to do it. Write all the other terms as powers of 10 with 1 subtracted. You will then have a series of powers of ten which is just a geometric series that I presume you have been taught how to sum. You should also be able to deal easily with all the minus ones.
2007-02-18 00:23:58 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Easy, write it as
10 - 1 + 100 - 1 + 1000 - 1 + ...... + 10^n - 1
10 + 100 + 1000 + .....+ 10^n - (1+1+1+...+n times)
First part is a Geometric Progression.
a = (10/9)(10^n - 1) - n
This is the sum for n number of terms.
2007-02-18 00:19:15 · answer #3 · answered by nayanmange 4 · 1⤊ 0⤋
Loosely speaking a is plus infinity (positive infinity)
Precisely speaking, 1) a is not defined 2) a does not exist 3) the value of a has no meaning.
2007-02-18 00:16:04 · answer #4 · answered by Sciman 6 · 0⤊ 0⤋
a = E (9 * m)
[Where E denotes 'sigma', 'sum of'
and m is in the order of 1, 11,111,1111....tends to infinity]
Am not able to use various symbols here, so just used the textual notations.
2007-02-18 00:23:52 · answer #5 · answered by Anonymous · 0⤊ 0⤋