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To be very concise, I am doing mechanics and, to my surprise,

$$\sum_{n=n_0-N+l}^{n_0+N}1 = 2N+1-l$$

Why is it so? Any help clarifying this would be very appreciated.

Rodrigo de Azevedo
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WorseThanEinstein
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    'Can you do Addition?' the White Queen asked. 'What's one and one and one and one and one and one and one and one and one and one?' – Angina Seng Apr 07 '19 at 18:10

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As the input of the summation is simply $1$ this effectively means that $$\sum_{n=a}^b1=\overbrace{1+1+1+...+1+1+1}^{b-a+1 \text{ times}}=b-a+1$$ So in your example $$\sum_{n=n_0-N+l}^{n_0+N}1=n_0+N-(n_0-N+l)+1=2N-l+1$$

Peter Foreman
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