simple mathematics so long as u think.
2007-03-29 09:09:42 · 6 answers · asked by tico 1 in Science & Mathematics ➔ Mathematics
5050
S = (n/2)*(a(1) + a(n))
= (100/2)(1 + 100)
= 50 * 101
= 5050
2007-03-29 09:13:05 · answer #1 · answered by Scott R 6 · 1⤊ 0⤋
Write the series backwards underneath itself:
1 2 3 ........................ 100
100 99 98 ....................... 1
(Can't do it properly in here, but I think you understand what I mean.)
Each vertical pair of numbers adds up to 101.
There are 100 pairs.
The total is therefore 100*101/2 = 10100 / 2 = 5050.
If you replace 100 by n, the number of terms in the general case, you get n(n+1)/2 for the sum of all integers from 1 to any number n.
2007-03-29 16:15:32 · answer #2 · answered by Anonymous · 0⤊ 0⤋
n*(n+1)/2
where n is the last number in the sequence.
for instance : 1 + 2 = 2*3/2 = 3
2007-03-29 16:14:17 · answer #3 · answered by gjmb1960 7 · 0⤊ 0⤋
this is what they called arithmetic series
=1/2*n*(n+1)
=1+2+3+4....+n
2007-03-29 16:25:35 · answer #4 · answered by Anonymous · 0⤊ 0⤋
sum (from 1 to n) = (1/2)(n+1)(n),
2007-03-29 16:13:19 · answer #5 · answered by sahsjing 7 · 0⤊ 0⤋
n(n+1)/2 where n is the number of terms.
But if you let this go to infinity, then the result is infinity.
2007-03-29 16:16:00 · answer #6 · answered by ironduke8159 7 · 0⤊ 0⤋