Monday

April 21, 2014

April 21, 2014

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

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!

**Related Questions**

College Alegbra - Prove by mathematical induction: ∑_(i=1)^n▒〖...

math - Use the method of differences to prove the following formulas 1) ∑_...

mathematics - ∫▒dx/(x√(2x^2+5x+1)) 2. ∫▒dx/(x&#...

AP Calc - Use mathematical induction to prove that the statement holds for all ...

Calculus - Use mathematical induction to prove that the statement holds for all ...

mathematical induction - solve this using the mathematical induction : 1/1(3)+1/...

chemistry - 1. Divide the ions below into 2 groups, those that tend to form ...

College Alegbra - Find the sum of the infinite geometric series given by ∑...

Pre-cal - use mathematical induction to prove that 1^2 + 2^2 + 3^2 + ... + n^2...

calculus - Find the trigonometric integral (a) ∫▒tan〖...