Saturday

April 18, 2015

April 18, 2015

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!

**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 ...

Math - Use mathematical induction to prove that 2^(3n) - 3^n is divisible by 5 ...

math : induction - The reversal of a string w, denoted w^R, is the string "...

math - Prove by mathematical induction that : E (3r-5)= 3n^2-7n /2 r=1