Prove that this statement is true?

Question

Use mathematical induction to prove that this statement is true for every positive n integer

 

2 + 7 + 12 + ... + (5n - 3) = n(5n - 1)/2

Answer 1

Let S be the sum in question. Each term is 5n-3

n=1  5×1-3=2

n=2  5×2-3=7, etc

We write n terms both forward and backward as

Note that the next to last term 5(n-1)-3=5n-8
S=2  +       7  +   12  + ...   + 5n-8+   5n-3

S=5n-3  + 5n-8+...             +    7    +   2    Add these two equations

2S = 5n-1+5n-1+    ...          + 5n-1+  5n-1  n-times 5n-1

2S=n(5n-1) and so S=(5n-1)/2

Verify by induction, as given by Arnold.

Answer 2

Let P(n) be the proposition: Σⁿ_i=1 (5i-3) = (n)(5n-1)/2.

(1) Basis step: show P(1) is true

(2) Inductive hypothesis: assume P(k) true

(3) Using (1) and (2) show P(k+1) true


Where are you getting stuck?