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8. Sequences and Series
hard
ગણ $\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid$ $n$ અને $2040$ નો ગુ.સા.અ $1$ થાય $\,\}$ ના બધાજ ઘટકોનો સરવાળો મેળવો.
A
$1251$
B
$1300$
C
$1456$
D
$1371$
(JEE MAIN-2021)
Solution
$2040=2^{3} \times 3 \times 5 \times 17$
$n$ should not be multiple of $2,3,5$ and $17 .$
Sum of all $n=(1+3+5 \ldots . .+99)-(3+9+15+21+\ldots . .+99)-(5+25+35+55+65$ $+85+95)-(17)$
$=2500-\frac{17}{2}(3+99)-365-17$
$=2500-867-365-17=1251$
Standard 11
Mathematics
