I don't understand the sigma notation and for loop

Question

I have the book saying that

and says that this is equivalent to saying

Answer 1

If you don't understand C code, it is because of mistakes in it.

It must be 1 instead of i in first case:

for(i = 1; i <= N; i++)
    Sum += 1;

It must be i instead of 1 and 1 instead of k there in the second case:

for(k = j; k <= i; k++)
    Sum += 1;

P.S. Also you have mistypo in the formula itself. 1 is skipped after Sigma by some reason. and j and i are swaped...

What is this book you are talking about?