Ex 4

discrete-ucozfree.comematics proof-writing induction
nói qua
Cite
Follow
edited Jan 7, năm ngoái at 19:55

6005
44k88 gold badges6868 silver badges157157 bronze badges
asked Feb 2, 2013 at 13:08

AndrewAndrew
8522 gold badges22 silver badges55 bronze badges
$endgroup$
2
địa chỉ cửa hàng a comment |

2 Answers 2

Sorted by: Reset to mặc định
Highest score (default) Date modified (newest first) Date created (oldest first)
4
$egingroup$
Your proof is fine, but you should show clearly how you got khổng lồ the last expression.

Bạn đang xem: Ex 4

$dfrack(k+1)(k+2)3+(k+1)(k+2)$

$=dfrack3(k+1)(k+2)+(k+1)(k+2)$

$=(dfrack3+1)(k+1)(k+2)$

$=dfrack+33(k+1)(k+2)$

$=dfrac(k+1)(k+2)(k+3)3$.

You should also word your proof clearly. For example, you can say "Let $P(n)$ be the statement ... $P(1)$ is true ... Assume $P(k)$ is true for some positive integer $k$ ... Then $P(k+1)$ is true ... Hence $P(n)$ is true for all positive integers $n$".

giới thiệu
Cite
Follow
edited Feb 2, 2013 at 16:55

Michael Hardy
1
answered Feb 2, 2013 at 13:15
user4594user4594
$endgroup$
2
địa chỉ cửa hàng a phản hồi |
0
$egingroup$
It might also be helpful to lớn go backwards to lớn see that it makes sense. Specifically, $$S_n+1 - S_n = frac(n+2)(n+1)(n)3 - frac(n+1)(n)(n-2)3 = frac13left(n^3 + 3n^2 + 2n - n^3 + n ight) = n(n+1)$$Going backwards, you can more easily see that $$S_n+1 = S_n + n(n+1)$$

tóm tắt
Cite
Follow
answered Mar 3, 2018 at 22:18

kaiwenwkaiwenw
4144 bronze badges
$endgroup$
showroom a bình luận |

Your Answer

Thanks for contributing an answer to lớn ucozfree.comematics Stack Exchange!

Please be sure to lớn answer the question. Provide details & share your research!

But avoid …

Asking for help, clarification, or responding lớn other answers.Making statements based on opinion; back them up with references or personal experience.

Xem thêm: Mẫu Đăng Ký Người Phụ Thuộc Giảm Trừ Gia Cảnh Qua Mạng 2021, Tờ Khai Đăng Ký Người Phụ Thuộc Giảm Trừ Gia Cảnh

Use ucozfree.comJax khổng lồ format equations. ucozfree.comJax reference.

To learn more, see our tips on writing great answers.

Draft saved
Draft discarded

Sign up or log in

Sign up using Google
Sign up using Facebook
Sign up using thư điện tử and Password
Submit

Post as a guest

Name
thư điện tử Required, but never shown

Post as a guest

Name
e-mail

Required, but never shown

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to lớn our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged discrete-ucozfree.comematics proof-writing induction or ask your own question.

Linked
7
computing $A_2=sum_k=1^nfrac1(z_k-1)^2 $ & $sum_k=1^n cot^2left( frackpin+1 ight)$
2
Bertrand's Box Paradox Generalized
Related
4
Proving by induction that $| x_1 + x_2 + ... + x_n | leq | x_1 | + | x_2| + ... + | x_n |$
0
Proof by induction; simplify when adding k+1th term. Understanding induction.
2
Prove by induction that $sum_i=0^n left(frac 3 2 ight)^i = 2left(frac 3 2 ight)^n+1 -2$
1
Induction Proof using factorials
2
Proving that $3 + 3 imes 5 + 3 imes 5^2 + cdots+ 3 imes 5^n = <3(5^n+1 - 1)> / 4$ whenever $n geq 0$
0
Induction to prove $a_n=2^n+1$
1
Proving $sum_i=1^n (1-frac1(i+1)^2) = fracn+22n+2$ using induction.
0
Proving $6n^4>(n+2)^4$ for $ngeq 4$, by induction
Hot Network Questions more hot questions

Question feed
Subscribe to RSS
Question feed khổng lồ subscribe lớn this RSS feed, copy & paste this URL into your RSS reader.

ucozfree.comematics
Company
Stack Exchange Network
Site kiến thiết / hình ảnh sản phẩm © 2022 Stack Exchange Inc; user contributions licensed under cc by-sa. Rev2022.5.9.42071

Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device & disclose information in accordance with our Cookie Policy.