Consider the following expression: (1 + x)n. A) Use the Binomial Theorem to find the first four terms of this polynomial. B) Why is 1 + nx a good approximation of this expression when x is less than 1?

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step-by-step explanation:

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week

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