(i) We prove "P(k + 1)(ii) We prove "If P(k) is true, then P(k+ 1) is true."SKILLS3-14 Proving a Formula Use mathematical induction to provethat the formula is true for all natural numbers n.- 1)2n (n + 1)21n(n+1)2"(n - 1)2"14. I + 2 +2-2 1 n(3n - 1)+ (3n- 2)24. 1+ 4+7+(n + 1)+n.2"[1 (n - 1)2"]se mathematical induction tot is true.++

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Asked Nov 26, 2019
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(i) We prove "P(k + 1)
(ii) We prove "If P(k) is true, then P(k+ 1) is true."
SKILLS
3-14 Proving a Formula Use mathematical induction to prove
that the formula is true for all natural numbers n.
- 1)
2n (n + 1)2
1
n
(n+1)
2"
(n - 1)2"
14. I + 2 +2
-2 1
help_outline

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(i) We prove "P(k + 1) (ii) We prove "If P(k) is true, then P(k+ 1) is true." SKILLS 3-14 Proving a Formula Use mathematical induction to prove that the formula is true for all natural numbers n. - 1) 2n (n + 1)2 1 n (n+1) 2" (n - 1)2" 14. I + 2 +2 -2 1

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n(3n - 1)
+ (3n- 2)
2
4. 1+ 4+7+
(n + 1)
+n.2"
[1 (n - 1)2"]
se mathematical induction to
t is true.
+
+
help_outline

Image Transcriptionclose

n(3n - 1) + (3n- 2) 2 4. 1+ 4+7+ (n + 1) +n.2" [1 (n - 1)2"] se mathematical induction to t is true. + +

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Expert Answer

Step 1

The given formula to be proved by the method of mathematical induction for all natural numbers n is,

n(3n-1)
1+47 (3n-2)=
2
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n(3n-1) 1+47 (3n-2)= 2

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Step 2

Prove that the statement is true when the value of n is 1.

1(3(1)-1)
RHS
2
= 1
1st term of the LHS
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1(3(1)-1) RHS 2 = 1 1st term of the LHS

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Step 3

Assume that the formula is true when the ...

k(3k-1)
( 3k - 2)=
2
1+4 7
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k(3k-1) ( 3k - 2)= 2 1+4 7

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