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8. sequence and series — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS8. sequence and series1 Mark
MCQ
The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ is
  • A
    $3000$
  • ✓
    $3050$
  • C
    $4050$
  • D
    None of these
✓

Answer

Correct option: B.
$3050$
b
(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 \times 2 + (50 - 1)2} \right\} + \frac{{20}}{2}\left\{ {2 \times 5 + (20 - 1)5} \right\}$

$ - \frac{{10}}{2}\left\{ {10 \times 2 + (10 - 1)10} \right\}$

$ = 2550 + 1050 - 550 = 3050$.

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