8. sequence and series — ગણિત ધોરણ 11 સાયન્સ — Question

Now, $24=2^{2} \cdot 3$

$\rightarrow \alpha$ is not the multiple of $2$ or $3$

Sum of values of $\alpha$

$= S ( U )-\{ S$ (multiple of $2$)$+ S$ (multiple of$3$ )

- $S$ (multiple of $6$)

$=(1+2+3+\ldots . .100)-(2+4+6 \ldots .+100)-(3$

$+6+\ldots . .99)+(6+12+\ldots .+96)$

$=\frac{100 \times 101}{2}-50 \times 51-\frac{33}{2} \times(3+99)+\frac{16}{2}(6+96)$

$=5050-2550-1683+816=1633$