I need help understanding why the two statements I have underlined with red are correct. I am confused as to how we can get $n + 1$.
And how $i \le n$ is true when it says $i < n$ in the while.
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4$\begingroup$ Please do not post images of text. $\endgroup$– Gilles 'SO- stop being evil'May 22, 2017 at 9:00
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2$\begingroup$ What exactly do you need help with? Do you know the definition of a loop invariant? What's stopping you checking that the statement satisfies the definition of being an invariant for the particular loop in the exercise? $\endgroup$– David RicherbyMay 22, 2017 at 10:01
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$\begingroup$ i know that a loop invariant is a statement that is true at any time in the loop. What i don't understand is how s = i(n+1) is it supposed to mean that n will grow with 1 for each iteration? $\endgroup$– LinexxlolMay 22, 2017 at 11:35
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2 Answers
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The loop invariant should hold before and after each iteration of the loop. In particular, it should hold before the loop starts and after it ends.
answered May 22, 2017 at 10:18
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Why $i \leqslant n$: because this program checks $i$ first and only then adds $+1$ to it.
When $s := s + i + x$ is applied, $x = n - i + 1$. Substituting $x$ to original formula we get $s := s + n + 1$. It is equal to $(n + 1) i$.
