Can u tell me the sum of
1^2007+2^2007+3^2007+............+2005^2007+2006^2007?
I asked someone this question and was struck.Can you solve
it for me elaborately with the method?
2006-09-24 19:11:06 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
infinity
2006-09-24 19:14:39 · answer #1 · answered by josef 2 · 0⤊ 0⤋
If your sum goes on indefinitely, the result is infinity.
But I suspect that you mean something like
1^2007 + 2^2007 + ... + 2006^2007 + 2007^2007...
then there is a method, but not an easy one. Compare
1 + 2 + 3 + ... + n = n(n+1)/2
1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6
1^3 + 2^3 + ... + n^3 = n^2 (n+1)^2/4
etc. For the case for 2007-th powers there is a polynomial of the 2008-th degree -- good luck finding it.
2006-09-24 19:20:54 · answer #2 · answered by dutch_prof 4 · 1⤊ 0⤋
If you included those ellipsis marks to mean that infinitely many terms of the form n^2007 are being added, then I guess the answer to your question would be infinity. Note that infinity is *NOT* a real number, but merely a symbol to stand for something arbitrarily large. In case you meant something like:
1^2007 + 2^2007 + 3^2007 + ... + n^2007,
then if you use one of the computer algebra systems such as Mathematica to obtain an explicit formula for this sum in terms of n, you get a polynomial of degree 2008 in n. Unfortunately, such formulae may not be amenable to "copy and paste" procedures because of limited computer system resources.
2006-09-24 22:37:30 · answer #3 · answered by JoseABDris 2 · 0⤊ 0⤋
6^2007+2007+2007
= 6^6021
2006-09-24 19:20:37 · answer #4 · answered by Rare Gem 3 · 0⤊ 0⤋
I tried to calculate this using Mathematica - the ultimate mathematics software available.
The result was shocking.
The formula was about 1000 lines (?) long. may be 5000. I never got through the shock.
My computer didnot allow me to copy it. The clipboard crashed.
Sorry, mate. But donot bother much about it. Why do you need it anyway?
2006-09-24 19:43:40 · answer #5 · answered by astrokid 4 · 0⤊ 0⤋
I think it would be infinity. Now because you did not put an upper bound to this function, the numbers just keep increasing and they never end.
2006-09-24 19:15:07 · answer #6 · answered by dancingcorpse 3 · 1⤊ 0⤋
i think the answer is infinity... just imagine adding 1, 2, 3 to the last number(if any)..
2006-09-24 20:54:18 · answer #7 · answered by ricorig 2 · 0⤊ 0⤋
the "......" indicates this goes on forever so the sum is infinite
2006-09-24 19:15:06 · answer #8 · answered by PC_Load_Letter 4 · 0⤊ 0⤋
use binominal theorem
2006-09-24 19:13:09 · answer #9 · answered by Brian 3 · 0⤊ 0⤋
do it yopurself or ask ur teacher...................
2006-09-24 20:51:33 · answer #10 · answered by Pummi 4 · 0⤊ 0⤋