Ex 8.1,10 - Chapter 8 Class 11 Binomial Theorem

Transcript

Ex 8.1,10 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 b0 + nC1 an 1 b1 + nC2 an 2 b2 + . . + nCn 1 a1 bn 1 + nCn a0 bn Hence (a + b)10000 = 10000C0 (a)10000 b0 + 10000C1 a9999 b1 + .. = 10000 0! 10000 0 ! a 10000 1 + 10000 ! 1!(10000 1)! a9999 (b)1 + = 10000! 1 10000! a10000 1 + 10000 9999! 1! 9999! a9999 b + = a10000 + 10000a9999 b + (a + b)10000 = a10000 + 10000a9999 b1 + Putting a = 1 & b = 0.1 (1 + 0.1)10000 = (1)10000 + 10000 (1)9999 (0.1)1 (1.1)10000 = 1 + 10000 (0.1)+ . = 1 + 1000.0 + . = 1001 + > 1000 Hence, (1.1)10000 is larger than 1000