Question

The sum of integers from 1 to 100 which is neither divisible by 2 nor by 3 is equal to​

Answer 1

Answer:

Number of multiples of 3 between 1 & 100 = [1003] = 33,

Number of multiples of 7 between 1 & 100= [1007] = 14,

Number of multiples of 21 between 1 & 100 = [10021] = 4,

Where [x] is the box function.

Sum of first 100 terms excluding terms divisible by 3 and 7:

S=∑i=1100i−3∑i=133i−7∑i=114i+21∑i=14i.

Apply the formula for ∑ni=1i and take it from here.