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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Example 3 Which is larger (1.01)1000000 or 10,000? (1.01)1000000 = (1 + 0.01)1000000 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)1000000 = 1000000C0 a1000000 b0 + 1000000C1 a999999 b1 +………….. = 1000000/0!(1000000 − 0)! a1000000 × 1 + (1000000 !)/(1!(1000000 − 1)!) a999999 b + …… = 1000000!/(1 × 1000000!) a1000000 + (1000000 × 999999 !)/(1 × 999999!) a999999 b + …… = a1000000 + 1000000a999999 b +……………… (a + b)1000000 = a1000000 + 1000000a999999 b +……………… Putting a = 1 & b = 0.01 (1 + 0.01)1000000 = (1)1000000 + 1000000 (1)99999 . (0.01) +……………… = 1 + 1000000 (1) × (0.01) +…………………… = 1 + 10000.00 +………………. = 10001 + …. > 10, 000 Hence , (1.01)1000000 is larger than 10,000

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.