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October 22

Step function

I realise that an integral is an infinite sum of a variable, for example $\lambda$ , with an infinitesimal parameter as a step value, for example $d\lambda$ :
$f(\lambda )=\int _{\lambda =0}^{\infty }{\frac {1}{\lambda ^{5}}}d\lambda$
I notice that $\lambda$ is here both a free and bounded variable.
So how can I do this, replacing an integral " $\int _{\lambda =0}^{\infty }...d\lambda$ " by a summation " $\sum _{\lambda =10}^{90}...\Delta \lambda$ ", where $\Delta \lambda$ is a finitesimal parameter acting as the step parameter? Malypaet (talk) 09:20, 22 October 2025 (UTC)[reply]

There's a Math Ref Desk. Abductive (reasoning) 10:17, 22 October 2025 (UTC)[reply]

Thanks Malypaet (talk) 12:03, 22 October 2025 (UTC)[reply]