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Ex 7.1, 10 Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000. (1.1)10000 = (1 + 0.1)10000 We know that (a + b)n = nC0 an + nC1 an – 1 b1 + nC2 an – 2 b2 + ….…. + nCn – 1 a1 bn – 1 + nCn bn Hence (a + b)10000 = 10000C0 a10000+ 10000C1 a9999 b1 +………….. = 10000/0!(10000 − 0)! a10000 × 1 + (10000 !)/(1!(10000 − 1)!) a9999 B +…… = 10000!/(1 ×10000!) a10000 × 1 + (10000 × 9999!)/(1! × 9999!) a9999 b +…………… = a10000 + 10000a9999 b +…………… (a + b)10000 = a10000 + 10000a9999 b +…………… Putting a = 1 & b = 0.1 (1 + 0.1)10000 = (1)10000 + 10000 (1)9999 (0.1) + …………… (1.1)10000 = 1 + 10000 (0.1)+…………. = 1 + 1000.0 + …………. = 1001 +………… > 1000 Hence, (1.1)10000 is larger than 1000

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo