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Since you want to start the summation starting at i=0 and the original summation starts at j=2 , you should make the substitution i=j-2 . Therefore, \sin(\sqrt{j})=\sin(\sqrt{i+2})=f(i) and the summation goes from i=0 to i=15 , i.e., \sum_{j=2}^{17}\sin(\sqrt{j})=\sum_{i=0}^{15}\sin(\sqrt{i+2})=\sum_{i=0}^{15}f(i).

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