<image>As shown in the image, there are geometric shapes numbered 1, 2, 3, ..., n. These geometric shapes are composed of several non-overlapping triangles. For example, the shape numbered 1 contains 1 triangle, the shape numbered 2 contains 4 non-overlapping triangles, the shape numbered 3 contains 7 non-overlapping triangles, etc. Observe the patterns in the shapes and solve the following problems:

(1) Write the number of non-overlapping triangles in the shape numbered n (expressed as an algebraic expression of n);
(2) If the shape numbered m contains 298 non-overlapping triangles, find the value of m;
(3) Let the number of triangles in the shape numbered 1 be denoted as \( S_{1} \). Let the number of non-overlapping triangles in the shape numbered 2 be denoted as \( S_{2} \), ..., and let the number of non-overlapping triangles in the shape numbered n be denoted as \( S_{n} \). Find the value of \( S_{2} - S_{3} + S_{4} - S_{5} + ... - S_{99} + S_{100} \).