At the age of eight, after correcting a school teacher's math blunder, the irritated teacher decided to humiliate Pascal and gave him this problem. "Take 1, add it to 2, then 3, then 4 on and on to 9,999." Mathematically it could be written: 1+2+3...+9999=?. Within seconds Pascal solved the problem in his head and spit out the answer, having had a brilliant insight. Can you do it in your head too? There's no way I can tell if you are cheating or not, but first right answer gets the prize!
2007-11-20 03:29:24 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
It's simple
1+ 2+ 3...+9999=x(variable)
9999+9998+9997... +1=x
________________________+
10.000+10.000+10.000...+10.000 = 2x
9999*10.000=2x
x= 9999.5000
= 49.995.000
2007-11-20 03:37:29 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Let x = 1 + 2 + 3... + 9999. Then:
2x=
....... 1 ..+...... 2 ...+ ..... 3... + 9999 (9999 terms)
+ 9999 ..+ 9998 ...+ 9997.... + ......1 (9999 terms)
= 10000 + 10000 + 10000... + 10000 (9999 terms)
= 10000*9999
So x = 5000*9999 = 49995000
By the way, that story didn't happen to me. It happened to Carl Frederich Gauss.
2007-11-20 11:42:26 · answer #2 · answered by Pascal 7 · 1⤊ 0⤋
10000*4999+5000=49995000... 1+9999 + 2+9998 + ...... + 4999+5001 + 5000
2007-11-20 11:35:39 · answer #3 · answered by Trevor H 3 · 1⤊ 0⤋
1+9999 =1000
2+9998 =1000
3+ 9997= 1000........in this problem there are, 4999.5 pairs. then : 4999.5*1000 = 49,995*10^3
2007-11-20 14:13:59 · answer #4 · answered by Eduardo (lalo) Leal 2 · 0⤊ 0⤋
50000000
I know his trick too... its quite easy.. and I did it in my head as well.
2007-11-20 11:35:30 · answer #5 · answered by Anonymous · 0⤊ 2⤋