Timeline for summing binomial coefficiens related
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1 at 13:05 | history | bounty ended | DXT | ||
| Mar 29 at 5:44 | comment | added | mathlove | @DXT : We already have $s_{n+1}+2s_n+s_{n-1}=0$ which can be written as $s_{n+1}+s_n=-(s_n+s_{n-1})$, so we get $s_{n+1}+s_n=(-1)^{n-1}(s_2+s_1)=2(-1)^{n-1}$. Dividing the both sides by $(-1)^{n+1}$ gives $t_{n+1}-t_n=2$ where $t_n=\frac{s_n}{(-1)^n}$. So, we get $t_n-t_1=2(n-1)$ which implies that $s_n=(-1)^nt_n=(-1)^n(2n+1)$. | |
| Mar 28 at 18:29 | comment | added | DXT | Thanks Mathlove for Nice Explanation. Can u please explain me How we get $\displaystyle s_{n}=(-1)^n(2n+1)$ without using Induction. | |
| Mar 28 at 16:51 | history | answered | mathlove | CC BY-SA 4.0 |