What is the sum of all the integers from 1 to 100 and how do you find it?
2006-12-25 14:36:45 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
5050
you take a sumation
put simply, its (101x100)/2
2006-12-25 14:41:07 · answer #1 · answered by bpsfm_2004 2 · 0⤊ 0⤋
Make 2 lists:
1 + 2 + 3 + .... + 99 + 100
100 + 99 + ... + 2 + 1
and add vertically. You get
101 + 101 + ... + 101 (100 terms)
100 x 101 is 10100, but since you added everything twice, divide by 2 to get 5050.
In general, sum of an arithmetic series is 1st term plus last term times half the number of terms. That's 2nd semester Alg 2, not calculus.
2006-12-25 22:49:02 · answer #2 · answered by Philo 7 · 1⤊ 0⤋
use gauss's formula n(n+1)/2
there are 100 numbers from 1 to 100.so n=100
S=n(n+1)/2=100 X 101/2 = 5050
2006-12-26 01:49:45 · answer #3 · answered by karthik p 1 · 0⤊ 0⤋
Like other users have answered, 1+2+...+k = k(k+1)/2. Also you can t evaluate 1+2^r+3^r+....+k^r by using bernulli numbers. See Calculus by M. Spivak .
....
2006-12-25 23:21:19 · answer #4 · answered by Terreno 2 · 0⤊ 0⤋
use the formula S = N * (N+1) / 2 and put N = 100 for the answer of 5050.... this is algebra and not calculus... either u are one of ur teachers is really crazy!!!
2006-12-25 23:13:42 · answer #5 · answered by Varun Reddy 1 · 0⤊ 0⤋
100
99+1=100
98+2=100
......
till
51+49=100
that makes 50 times 100
remaining no. is 50
answer 5050.
2006-12-25 22:43:09 · answer #6 · answered by moksha 2 · 0⤊ 1⤋
That depends. If so, the answer is zero.
2006-12-25 22:47:29 · answer #7 · answered by nightowl 2 · 0⤊ 1⤋