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whats one over one plus one over two plus one over three so on forever you keep adding positive values so maybe its infinity but the numbers are getting smaller and smaller so maybe this sum is finite heres the one represented as an area heres the one half as an area the one-third and so on forever and heres the function one over x graphed from one to infinity notice how the rectangles line up nicely and more importantly notice that the area of the rectangles is larger than the area under the curve of the function you can use technology or calculus to find the area under this curve and realize its infinite yet the area of the rectangles is bigger than that since the area of the rectangles represent our sum we have our answer so now what if i ask you this question