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Q.
The sum of those integers from $1 $ to $100$ which are not divisible by $3$ or $5$ is
Sequences and Series
Solution:
First number $=1$
Last number $=100$
Sum of integer 1 to 100
$S=\frac{100}{2}[101]=5050$
numbers which are divisible by 3 are $3,6,9................. 99$
$S _1=\frac{33}{2}[3+99]=33 \times 51=1683$
numbers which are divisible by 5 are $5,10 \ldots \ldots \ldots ., 100$
$S _2=\frac{20}{2}[105]=1050$
numbers which are divisible by 3 and 5 both are $15,30 \ldots \ldots . .90$
$S _3=\frac{6}{2}[15+90]=3(105) =315$
Now sum of integers which are not divisible by 3 or 5
$=S-S_1-S_2+S_3 =5050-1683-1050+315=2632$