The sum of integers from 1 to 100 that are di | vedclass

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Question

(b) The sum of integers from $1$ to $100$ that are divisible by $2$ or $5 =$ sum of series divisible by $2 +$ sum of series divisible by $5 -$ sum of

Vedclass · Accepted Answer

$3050$

Vedclass · Answer

(b) The sum of integers from $1$ to $100$ that are divisible by $2$ or $5 =$ sum of series divisible by $2 +$ sum of series divisible by $5 -$ sum of series divisible by $2$ and $5$.

$ = (2 + 4 + 6 + ...... + 100) + (5 + 10 + 15....... + 100)$

$ - (10 + 20 + 30 + ........ + 100)$

$ = \frac{{50}}{2}\left\{ {2 	imes 2 + (50 - 1)2} ight\} + \frac{{20}}{2}\left\{ {2 	imes 5 + (20 - 1)5} ight\}$

$ - \frac{{10}}{2}\left\{ {10 	imes 2 + (10 - 1)10} ight\}$

$ = 2550 + 1050 - 550 = 3050$.

The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ is

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