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cptstubing
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Homework Statement
A step in this process of proving Sn: 1+4+7+...+(3n-2) = n(3n-1)/2
confuses me. I hope someone can clarify this for me.
I do not require the work done, I need clarification on a step only. Thanks!
Homework Equations
After assuming n=k, we say Sk: 1+4+7+...+(3k-2) = k(3k-1)/2
When assuming n=k+1, we say Sk+1: 1+4+7+...+(3k-2) + (3k+1) = k(3k-1)/2 + (3k+1)
The book states the reason for adding (3k+1) on both sides of the equation is because 3(k+1)-2 = 3k+1
The Attempt at a Solution
Why is this the case? What is 3(k+1)-2 ? I know it equals 3k+1 because 3 multiplied by (k+1) is 3k+3, then -2 makes it 3k+1. But where did 3(k+1)-2 suddenly come from? It seems arbitrary and is without explanation in the textbook.
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