Gujarati
8. Sequences and Series
medium

$1$ व $100$ के बीच के उन सभी पूर्णाकों का योगफल जो कि $3$ व $5$ से विभाजित न हों  

A

$2489$

B

$4735$

C

$2317$

D

$2632$

Solution

(d) माना $S = 1 + 2 + 3 + ……….. + 100$

$ = \frac{{100}}{2}(1 + 100) = 50(101) = 5050$

माना ${S_1} = 3 + 6 + 9 + 12 + ……… + 99$

= $3(1 + 2 + 3 + 4 + ……… + 33)$

= $3.\frac{{33}}{2}(1 + 33) = 99 \times 17 = 1683$

माना ${S_2} = 5 + 10 + 15 + …….. + 100$

= $5(1 + 2 + 3 + …….. + 20)$

= $5.\frac{{20}}{2}(1 + 20) = 50 \times 21 = 1050$

माना ${S_3} = 15 + 30 + 45 + …….. + 90$

= $15(1 + 2 + 3 + …….. + 6)$

= $15.\frac{6}{2}(1 + 6) = 45 \times 7 = 315$

अभीष्ट योग  =$S – {S_1} – {S_2} + {S_3}$

= $5050 – 1683 – 1050 + 315 = 2632.$

 

Standard 11
Mathematics

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