Question

10.Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.

Answer 1

The given number ( 1.1 ) 10000 or 1000 we have to find which number is larger using Binomial Theorem

The formula for binomial expansion is ,

. ( a+b ) n = C n 0 a n + C n 1 a n−1 b+ C n 2 a n−2 b 2 +..........+ C n n−1 a. b n−1 + C n n b n (1)

For applying binomial theorem we have to split 1.1 into ( 1+0.1 ) .

( 1.1 ) 10000 = ( 1+0.1 ) 10000 (2)

On comparing the equations (1) and (2), values of a=100, b=0.1 and n=10000 .

( 1.1 ) 10000 = ( 1+0.1 ) 10000 = C 10000 0 + C 10000 1 ( 1.1 )+other positive terms =1+10000×1.1+other positive terms =1+11000+other positive terms >1000

Thus from the expansion we find that ( 1.1 ) 10000 >1000 .