# How do you use the binomial theorem to approximate the value of #1.07^7# ?

##### 1 Answer

May 9, 2016

#### Explanation:

By the binomial theorem we have:

#(a+b)^7 = sum_(k=0)^7 ((7),(k)) a^(7-k)b^k#

where

We can get these binomial coefficients from the row of Pascal's triangle that begins

So:

#(a+b)^7 = a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7#

Putting

#1.07^7 ~~ 1+7(0.07)+21(0.07)^2+35(0.07)^3+35(0.07)^4+21(0.07)^5#

#=1+7(0.07)+21(0.0049)+35(0.000343)+35(0.00002401)+21(0.0000016807)#

#=1+0.49+0.1029+0.012005+0.00084035+0.0000352947#

#~~1.60578#