What is the formula that will solve for
1+2+3+4+5+ . . . etc to any number? Explain.
2007-11-30 07:29:39 · 12 answers · asked by bbmm 4 in Science & Mathematics ➔ Mathematics
Let S be the sum from 1 to some integer n so
S = 1 + 2 + 3+ ....+ (n-2)+(n-1)+n which written backwards is
S= n+(n-1)+(n-2)...... + 3 + 2 + 1 and adding vertically is
2S= n+1)+(n+1)+(n+1) ...(n+1)+(n+1)+(n+1) or n of the (n+1)s
There fore 2S = n(n+1) and dividing by 2 gives your formula
S = n(n+1)/2 so for example 1+2+3+4+5+6 would be
S = 6(6+1)/2 = 21 which checks out.
Gauss found this formula in first grade as I recall.
2007-11-30 07:32:39 · answer #1 · answered by baja_tom 4 · 1⤊ 2⤋
1 + 2 + 3 + ... + n = ( n ) ( n + 1 ) / 2
2007-11-30 15:33:59 · answer #2 · answered by jgoulden 7 · 1⤊ 2⤋
N(n+1)/2
1+2+3+4+5+ 6+
to add the sum of 6
we can use 6(6+1)/2 = 21
2007-11-30 15:36:08 · answer #3 · answered by surmy 2 · 1⤊ 1⤋
Let tn represent the term *n is a subscript*
example : t1 = 1 ; t2 = 2
tn = tn -1 + 1 *n -1 is subscript*
to find t4
t4 = t4 -1 + 1 *4 -1 is subscript*
t4 = 3 + 1
t4 = 4
2007-11-30 15:49:46 · answer #4 · answered by Kidus 1 · 0⤊ 1⤋
1+ 2 + 3 + 4 + 5 + ..... upto ...... + n
= n(n + 1)/2
2007-11-30 15:35:36 · answer #5 · answered by sv 7 · 1⤊ 1⤋
n*(n+1)/2
:-)
2007-11-30 15:33:56 · answer #6 · answered by Anonymous · 1⤊ 2⤋
formula: n+1
2007-11-30 15:36:50 · answer #7 · answered by tramimaus 4 · 0⤊ 2⤋
Answer: n = n + 1
2007-11-30 15:35:07 · answer #8 · answered by Jun Agruda 7 · 3⤊ 2⤋
n+1, n is the number you have and your adding one, the pattern shows how you are increasing. geometry??
2007-11-30 15:40:02 · answer #9 · answered by no_duh ツ 4 · 1⤊ 1⤋
= n+1, put in n is your number and it will keep increasing.
2007-11-30 15:32:32 · answer #10 · answered by rcds23 6 · 0⤊ 3⤋