induction help PLZ! (1 Viewer)

[koolkid59]

For the 'divisibility by integar' Qs
plz do Q 6-10 with full working and some explanation so i can understand how you do these types of Qs
Similarly, for the other attachment....plz do Q11,14 and 15.......also what do these weird symbols in Q11 and 14 mean?
plz do these ASAP!!!!!!

 

[math man]

i dont have time to answer them now, but Q11,14 have sigma notation, which means the sum of...so what you can do to make it easier for yourself is to expand the series by subbing in each value from the starting value on the bottom to the last value on the top, then it just becomes a normal induction question. A hint to do division questions is in the assume true for n=k step you let it equal to aM, where a is what you are trying to prove it is divisible by, say 7, and M is just some constant..then in the prove n=k+1 step you sub this in and manipulate the expression to be divisible by a.

 

[Deep Blue]

Mate, I could do worked solutions for all of these questions but I don't think that would bridge the gap in your understanding, and besides I am hopeless at latex. I will try and explain it though. Have you done questions like these before? For the divisibility proofs, do your n=1 step, then for your n=k step, assume something like, for example in Q6,






Hence true for n=k+1, therefore true for all integers n≥1 by mathematical induction.

So basically, it's just a rearrangement of the assumption step and direct substitution and then manipulation.
As for those weird symbols, that is sigma notation. Basically it means, the sum of all the values between k=1 (or whatever number is given at the bottom) and n (or whatever number is given at the top) when they are substituted into the following equation. Does that make sense?

 

[D94]

As a brief example, the first one:


You just need to apply the same process for your other questions. If we do them all for you, you won't have a full understanding of how to do this. In the exam, you'd lose 4-6 marks if you don't know how to do these questions.

 

[AAEldar]

Questions 6-10

Questions 11, 14, 15

 

[koolkid59]

thank u guys sooo much for taking time to help me
keep up the great effort!

 

[CH0C0LAT3BEAR]

plz do these ASAP!!!!!!

Just LOL.