# Ex 4

discrete-ucozfree.comematics proof-writing induction
nói qua
Cite
Follow
edited Jan 7, năm ngoái at 19:55 6005
asked Feb 2, 2013 at 13:08 AndrewAndrew
\$endgroup\$
2
địa chỉ cửa hàng a comment |

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
\$endgroup\$
showroom a bình luận |

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

But avoid

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

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

Draft saved

Submit

### Post as a guest

Name
thư điện tử Required, but never shown

### Post as a guest

Name
e-mail

Required, but never shown

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

7
computing \$A_2=sum_k=1^nfrac1(z_k-1)^2 \$ & \$sum_k=1^n cot^2left( frackpin+1 ight)\$
2
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 