Use mathematical induction to prove the formula for all integers n ≥ 1. 1 + 6 + 11 + 16 + ... + (5n-4)=(5n - 3). Find S₁ when n = 1. S₁ = Assume that Sk = 1 + 6 + 11 + 16 + ... + (5k − 4) = ½ (5k − 3). Then, Sk+ 1 = Sk+ªk+ 1 = (1 + 6 + 11 + 16 + ... + ak+1= Use the equation for ak + 1 Sk+1= (5k − 4)) + ªk + 1* and S to find the equation for Sk + 1* k Is this formula valid for all positive integer values of n? Yes No
Use mathematical induction to prove the formula for all integers n ≥ 1. 1 + 6 + 11 + 16 + ... + (5n-4)=(5n - 3). Find S₁ when n = 1. S₁ = Assume that Sk = 1 + 6 + 11 + 16 + ... + (5k − 4) = ½ (5k − 3). Then, Sk+ 1 = Sk+ªk+ 1 = (1 + 6 + 11 + 16 + ... + ak+1= Use the equation for ak + 1 Sk+1= (5k − 4)) + ªk + 1* and S to find the equation for Sk + 1* k Is this formula valid for all positive integer values of n? Yes No
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Use mathematical induction to prove the formula for all integers n ≥ 1.
1 + 6 + 11 + 16 + ... + (5n = 4) = (5n
-
(5n
- 3).
2
Find S₁ when n = 1.
S₁ =
Assume that
k
= 1 + 6 + 11 + 16 + ··· + (5k – 4) =
+ (5k - 4) =(5k - 3).
2
Sk
Then,
Sk+1 = Sk+ªk+1 = (1 + 6 + 11 + 16 +
TELE
..
ak+1=
+ (5k − 4)) + ªk+1°
Use the equation for ak + 1 and S to find the equation for Sk+
k
1ª
Sk+1=
Is this formula valid for all positive integer values of n?
O Yes
O No
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