## cinar Group Title discrete math question..need some help.. one year ago one year ago

1. cinar Group Title

2. cinar Group Title

any idea..

3. amistre64 Group Title

sounds inductiony to me

4. cinar Group Title

actually I found general formula for sum, but I am not sure if I can use it as a proof..

5. amistre64 Group Title

can you work it up to the formula? then once a general formula is "determined" you might be able to prove it by induction

6. amistre64 Group Title

of course, you might have a better notion of what you need. What are your thoughts on it? what have you been thinking would work?

7. cinar Group Title
8. cinar Group Title

You see the poly is always m+1 degree when expression is m degree

9. cinar Group Title
10. amistre64 Group Title

that looks like a binomial expansion to me

11. amistre64 Group Title

$\sum(n+1)^k=\binom{k}{0}n^k1^{0}+\binom{k}{1}n^{k-1}1^1+\binom{k}{2}n^{k-2}1^2+...+\binom{k}{k}n^{k-k}1^k$

12. amistre64 Group Title

n=0,1,2,3,... produces the same summation i bleieve as:1^k + 2^k + 3^k + ...

13. cinar Group Title

can we use this notation$\sum_{n=0 }^k(n+1)^k=\binom{k}{n}n^k1^{0}+\binom{k}{n+1}n^{k-1}1^1+\binom{k}{n+2}n^{k-2}1^2+...+\binom{k}{n+k-1}n^{k-k}1^k$

14. cinar Group Title

I guess n should be start from 1

15. cinar Group Title

can we use this notation$\sum_{i=1 }^n i^k=1^k+2^k+......+n^k=?$

16. cinar Group Title

17. amistre64 Group Title

something that bugs me about what i posted is that if n=0, we run into a 0^0 case ....

18. amistre64 Group Title

im not read up n the bernuolli numbers enough to comment if thats a suitable "showing" or not

19. amistre64 Group Title

i^1; show a second degree poly 1,3,6,10,15 2 3 4 5 1 1 $1+2n+\frac{n(n-1)}{2!}~:~n=0,1,2,3,...$ is a 2nd degree poly i^2; show a third degree poly 1 5 14 30 55 4 9 16 25 5 7 9 2 2 $1+4n+5\frac{n(n-1)}{2!}+2\frac{n(n-1)(n-2)}{3!}~:~n=0,1,2,3,...$is a 3rd degree poly

20. amistre64 Group Title

if we can construct this polynomial as a pattern; then we can try to induct that pattern to the k+1th term or would we have to prove that each substructure is inductable? this is the part i hate about proofs, you never know when you have to reinvent the wheel

21. cinar Group Title

thanks, you helped me a lot..