Hi, I tried everything I could think of, but I cannot solve this problem. Any idea? (look at the image bellow)

Attachment 24865

Printable View

- Sep 20th 2012, 05:06 AMalireza1992Problem with mathematical induction
Hi, I tried everything I could think of, but I cannot solve this problem. Any idea? (look at the image bellow)

Attachment 24865 - Sep 20th 2012, 05:38 AMemakarovRe: Problem with mathematical induction
In the inductive step, you need to show $\displaystyle \frac{1-\cos2n\theta}{2\sin\theta}+\sin(2n+1)\theta=\frac{ 1-\cos(2n+2)\theta}{2\sin\theta}$. Multiply both sides by $\displaystyle 2\sin\theta$ and use the formula for the difference of cosines.