voko said:Are there any restrictions on q and b? Otherwise the statement is trivially satisfied by q = n, b = 1, r = 0.
voko said:Are there any restrictions on q and b? Otherwise the statement is trivially satisfied by q = n, b = 1, r = 0.
You can easily check that it's true for [itex]n = 0[/itex]. Now suppose it's true for [itex]n[/itex], so there exist [itex]q[/itex] and [itex]r < b[/itex] such that [itex]n = qb + r[/itex]. Now consider [itex]n + 1[/itex]. A reasonable first step would be to add 1 to both sides of the equation above:zjhok2004 said:Can someone help me on how to solve this question? and how does induction works here?
thank you
When approaching an Apostol Calculus proof, it is important to first understand the given problem and the concepts involved. Then, break down the proof into smaller, more manageable steps and use logical reasoning to connect them. It is also helpful to refer to previous theorems and definitions to guide your reasoning.
Some common mistakes to avoid when solving Apostol Calculus proofs include not fully understanding the given problem, skipping steps or making assumptions without proper justification, and using incorrect notation or symbols. It is also important to double check your calculations and reasoning for accuracy.
The best way to improve your skills in solving Apostol Calculus proofs is to practice regularly and seek help from your peers or a teacher when needed. It is also helpful to read and fully understand the theorems and concepts related to the proof, and to review and analyze proofs that have been previously solved.
To ensure the correctness of your Apostol Calculus proof, you should first check if all the given conditions and assumptions are satisfied. Then, carefully review each step of your proof to ensure that it follows logically from the previous steps. Lastly, you can also ask for feedback from a peer or teacher to confirm the validity of your proof.
There are various resources available for help with Apostol Calculus proofs, including textbooks, online forums and communities, tutoring services, and study groups. Your teacher or professor may also be able to provide additional resources or guidance. It is important to utilize these resources to improve your understanding and skills in solving Apostol Calculus proofs.