Question
Download Solution PDF10 × 20 × 30 × ... × 1000
में शून्य की संख्या ज्ञात कीजिए
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
10 × 20 × 30 × ... × 1000
प्रयुक्त अवधारणा:
प्रत्येक में से 10 उभयनिष्ट लें।
n! में अनुगामी शून्य की संख्या = n को 5 से विभाजित करें, इस प्रक्रिया को तब तक जारी रखें जब तक हमें वह मान नहीं मिल जाता जो 5 से कम है। अब सभी भागफलों को जोड़ेंऔर परिणामी संख्या शून्यों की संख्या होगी।
गणना:
10 × 20 × 30 × ... × 1000
⇒ (10 × 1) × (10 × 2) × (10 × 3) × (10 × 4) ..........× (10 × 100)
⇒ 10100 × (1 × 2 × 3 × ... × 100)
⇒ 10100 × (100!)
शून्य की संख्या = 100 + {(100)/5 + (20)/5}
⇒ 100 + 20 + 4
⇒ 124
∴ 10 × 20 × 30 × ... × 1000 में अनुगामी शून्य की संख्या 124 है।
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