Find the sum

Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5

Correct result:

s =  3050

Solution:

$$\begin{gathered} 2,4,6,8,\dots ,100 \\ 5,10,15,\dots ,100 \\ {s}_1=2\cdot (1+2+3+4\dots +50) \\ {s}_1={\displaystyle \frac{n_1}{2}}\cdot (a_{50}+a_1) \\ {s}_1={\displaystyle \frac{50}{2}}\cdot (100+2)=2550 \\ {s}_2=5(1+3+5+\dots +19) \\ {s}_2={\displaystyle \frac{n_2}{2}}\cdot (b_{19}+b_1) \\ {s}_2={\displaystyle \frac{10}{2}}\cdot (95+5)=500 \\ s=s_1+s_2=2550+500=3050 \end{gathered}$$

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