Posted by **Iman** on Tuesday, April 17, 2012 at 4:01pm.

3. Prove by induction that∑_(r=1)^n▒〖r(r+4)=1/6 n(n+1)(2n+13)〗.

5. It is given that u_1=1 and u_(n+1)=3u_n+2n-2 where n is a positive integer.

Prove, by induction, that u_n=3^n/2-n+1/2.

14. The rth term of a sequence is given by u_r=r(3r+1),r=1,2,3,…

i) Write down the values of ∑_(r=1)^n▒u_r for n=1,2,3, and 4.

ii) Make a conjecture for a formula for ∑_(r=1)^n▒u_r , giving your answer in the form nf(n), where f(n) is a function of n.

iii) Prove by induction a formula for ∑_(r=1)^n▒u_r .

If the text isn't displaying properly, please use my screenshot.

i44.tinypicDOTcom/66dwnb.png

Sorry about the inconvenience, and thanks!

## Answer this Question

## Related Questions

- College Alegbra - Prove by mathematical induction: ∑_(i=1)^n▒〖...
- math - Use the method of differences to prove the following formulas 1) ∑_...
- Calculus - Use mathematical induction to prove that the statement holds for all ...
- AP Calc - Use mathematical induction to prove that the statement holds for all ...
- Computer proof - Prove by induction on all positive integer k that if m is any ...
- mathematics - ∫▒dx/(x√(2x^2+5x+1)) 2. ∫▒dx/(x&#...
- pre calc - Use mathematical induction to prove that the statement is true for ...
- pre calc - Use mathematical induction to prove that the statement is true for ...
- pre-calc - Use mathematical induction to prove that the statement is true for ...
- Math - Use mathematical induction to prove that 2^(3n) - 3^n is divisible by 5 ...

More Related Questions