A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
prove using mathematical induction
\[x ^{n}  y^{n} = (xy)(x^{n1} + x^{n2}y +.....+ xy^{n2} + y^{n1}\]
I'm not even able to prove it true for n =1 .
How could one reduce the term in the second bracket to 1 ?
 2 years ago
prove using mathematical induction \[x ^{n}  y^{n} = (xy)(x^{n1} + x^{n2}y +.....+ xy^{n2} + y^{n1}\] I'm not even able to prove it true for n =1 . How could one reduce the term in the second bracket to 1 ?

This Question is Closed

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1343194234112:dw

panlac01
 2 years ago
Best ResponseYou've already chosen the best response.0fundamental theorem of algebra

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2n=1 is the base case

panchtatvam
 2 years ago
Best ResponseYou've already chosen the best response.0@experimentX 1 is the base case but it also has to be proved first.

panchtatvam
 2 years ago
Best ResponseYou've already chosen the best response.0I'm unable to reduce the expression in the second bracket as it involves inverse terms with dont cancel to 1

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2in your formula n1 > 0, but n1 =0 for n=1

A.Avinash_Goutham
 2 years ago
Best ResponseYou've already chosen the best response.1well u can do it this way.......... (xy)(x^n+y^n+.....) (x^(n)  y^(n))(xy)+ y(xy)(xn−1+xn−2y+.....+xyn−2

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1343194693791:dw

A.Avinash_Goutham
 2 years ago
Best ResponseYou've already chosen the best response.1@experimentX is that the final step?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2no .. not really, currently, i cannot think using induction.

A.Avinash_Goutham
 2 years ago
Best ResponseYou've already chosen the best response.1no it's purely based on induction.....

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2it proves directly using geometric sum

A.Avinash_Goutham
 2 years ago
Best ResponseYou've already chosen the best response.1u prove very dumb things using induction/by contradiction...........

A.Avinash_Goutham
 2 years ago
Best ResponseYou've already chosen the best response.1so now by induction.....we have xn−yn=(x−y)(xn−1+xn−2y+.....+xyn−2+yn−1 by induction

A.Avinash_Goutham
 2 years ago
Best ResponseYou've already chosen the best response.1nd we need to prove xn+1−yn+1=(x−y)(xn+xny+.....+xyn1+yn......

A.Avinash_Goutham
 2 years ago
Best ResponseYou've already chosen the best response.1so try showing that (x−y)(xn+xny+.....+xyn1+yn...... = xn+1−yn+1

panchtatvam
 2 years ago
Best ResponseYou've already chosen the best response.0if we follow induction methods then as per @experimentX the formula is valid only for natural indexes . so n =1 gets proved . for n+1 could be proved by solving the RHS instead of adding any term to the value for the equation for n.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1343195660262:dw i guess ... certainly, other ways are more intuitive

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2\[ (xy)(x^n + x^{n1}y + x^{n2}y^2 + ... +y^n) \\ = x^n(xy) + y (xy)(x^{n1}+x^{n2}y + ...+y^{n2}) \\ = x^n(xy)+y (x^n  y^n) = x^{n+1}  y^{n+1}\]

panchtatvam
 2 years ago
Best ResponseYou've already chosen the best response.0I wanted to have a mathematical Induction proof of the problem . But as it comes out the problem needs to have certain assumptions and can't be explained using mathematical induction in the normal way. Assumptions : 1. n > 1 so as shown by @experimentX we need to work the problem from RHS to LHS to prove the second condition of the induction thoerem.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.