The binomial theorem states that for any number n and any x with (a) Show that if n is a positive…

 The binomial theorem states that for any number n and any x with

(a)    Show that if n is a positive integer, this infinite series terminates (that is, has only a finite number of nonzero terms) . write the series down explicitly for the cases n = 2 and n = 3 (b) write down the binomial series for the cases n = -1 This case give an infinite series for 1/(+ x) , but when x is small, you get a good approximation if you keep just  the first  two   terms:

As quoted in (3.6 ) calculate both sides of this approximation for each of the values x = 0.5,0.1 and 0.01 and in each case find the percentage by which the approximation (1-x) differ from the exact value 1/(1+x )

 

 

 

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