Mathematical Induction
posted by Anon
Use mathematical induction to prove that the following is true.
8+11+14...+(3n+5)=1/2n(3n+13), for all n in the set of natural numbers.

Steve
prove that P(1) is true:
8 = 1/2 1(3*1+13) = 16/2 = 8
Assuming P(k), see what P(k+1) means:
8+11+...+(3k+5)+(3(k+1)+5) = k/2 (3k+13) + (3(k+1)+5)
= k/2 (3k+13) + 3k+8
1/2 (3k^2+13k + 6k+16)
= 1/2 (3k^2+19k+16)
= 1/2 (k+1)(3k+16)
= 1/2 (k+1)(3(k+1)+13)
= P(k+1)
So, P(1) and P(k) ==> P(k+1)
Respond to this Question
Similar Questions

Math
Use mathematical induction to prove that 5^(n)  1 is divisible by four for all natural numbers n. Hint: if a number is divisible by 4, then it has a factor of 4. also, 1 = 5 +4 This is a take home test so I don't want the answer … 
Math  Mathematical Induction
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+2n2 where n is a positive integer. Prove, by induction, that u_n=3^n/2n+1/2. 14. The rth term of … 
AP Calc
Use mathematical induction to prove that the statement holds for all positive integers. Also, can you label the basis, hypothesis, and induction step in each problem. Thanks 1. 2+4+6+...+2n=n^2+n 2. 8+10+12+...+(2n+6)=n^2+7n 
Calculus
Use mathematical induction to prove that the statement holds for all positive integers. Also, label the basis, hypothesis, and induction step. 1 + 5 + 9 + … + (4n 3)= n(2n1) 
Mathematical induction. I'm stuck. So far I have..
For all integers n ≥ 1, prove the following statement using mathematical induction. 1+2^1 +2^2 +...+2^n = 2^(n+1) −1 Here's what I have so far 1. Prove the base step let n=1 2^1=2^(1+1)1 False. Someone else suggested that … 
Algebra ASAP
so this is a fill in on a worksheet and I am having difficulty as the ones I inserted are incorrect can anybody help me how to do it all, sorry it's a long problem. Show that 3^2n − 1 is divisible by 8 for all natural numbers … 
precalculus
Can you please check my answers? 1.Find Pk + 1 if Pk=2^K1/k! answer: 2^k+1/(k+1)! 2.Find Pk + 1 if Pk = 7 + 13 + 19 + ...+[6(k  1)+1] + (6k + 1) answer: 7+13+9...(6k1+1)+6k+1 +(6k+2) 3.What is the first step when writing a proof 
precalculus
Find Pk + 1 if Pk = 7 + 13 + 19 + ...+[6(k  1)+1] + (6k + 1) 7 + 13 + 19 + …+[6(k  1) + 1] + (6k + 1) + [6(k + 1) + 1] 8 + 14 + 20 + …+[7(k  1) + 1] + (7k + 1) 7 + 13 + 19 + …+(6k + 1) 7 + 13 + 19 + ...+[6(k  1) + 1] + (6k7 … 
Mathematical Induction
I have been given that a1 = 1 and an+1 = 1/3*(an + 4). In order to prove that this sequence is monotonous, what is the second step of mathematical induction? 
Math..mathematical induction
Prove by mathematical induction that 1+3+5+7+....+(2n1)=n²