bored.of.u
Member
- Joined
- Jul 21, 2008
- Messages
- 236
- Gender
- Male
- HSC
- 2010
Need help with a question guys
Prove by mathematical induction that for all positive integers n and many n real numbers x<SUB>1</SUB>, x<SUB>2</SUB> … x<SUB>n</SUB> there exist real numbers a<SUB>1</SUB>, a<SUB>2</SUB> … a<SUB>n</SUB> with each l<SUB> </SUB>a<SUB>i </SUB>l < 1 (absolute values of a<SUB>i </SUB>are less than or equal to one)<SUB> </SUB>such that
sin ( x<SUB>1</SUB> + x<SUB>2</SUB> + … + x<SUB>n</SUB>) = a<SUB>1</SUB>sin x<SUB>1</SUB> + a<SUB>2</SUB> sin x<SUB>2</SUB> + … + a<SUB>n</SUB> sin x<SUB>2</SUB>
Prove by mathematical induction that for all positive integers n and many n real numbers x<SUB>1</SUB>, x<SUB>2</SUB> … x<SUB>n</SUB> there exist real numbers a<SUB>1</SUB>, a<SUB>2</SUB> … a<SUB>n</SUB> with each l<SUB> </SUB>a<SUB>i </SUB>l < 1 (absolute values of a<SUB>i </SUB>are less than or equal to one)<SUB> </SUB>such that
sin ( x<SUB>1</SUB> + x<SUB>2</SUB> + … + x<SUB>n</SUB>) = a<SUB>1</SUB>sin x<SUB>1</SUB> + a<SUB>2</SUB> sin x<SUB>2</SUB> + … + a<SUB>n</SUB> sin x<SUB>2</SUB>
