for use in the rest of this chapter. Exercise 15A Complete all the rows of Pascal's triangle for n = ni m FOUNDATIO = 0, 1, 2, 3, .. ., 12. Keep this in a prominent place

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Chapter13: Sequences And Series
Section13.6: The Binomial Theorem
Problem 56E
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15A Binomial expansions and Pascal's triangle
Complete all the rows of Pascal's triangle forn = 0, 1, 2, 3, .. . , 12. Keep this in a prominent place
for use in the rest of this chapter.
ni nol o
FOUNDATIO
Exercise 15A
%3D
. Using Pascal's triangle to provide the binomial coefficients, give the expansions of:
a (1 + x)6
b (1 – x)6
C ( 1 + x)
d (1 - x)°
e (1 + c)5
f (1+ 2y)*
h (1 – 3z)
(1-)*
8
(1 +)*
5
lo sulsk
(1+
(1 +
3x\4
ontinue the calculations of the expansions of (1 + x)" at the beginning of this section, expanding
+ x)' and (1 + x)° in the same manner. Keep your work in columns, so that the addition prope
Pascal's triangle is clear.
the specified term in each expansion.
gcbonqour of
i ind the term in x',
or (1 + x)":
b For (1 - x)':
where 0
in x?,
find the term in x°.
find the term
ii find the term in r5
Transcribed Image Text:15A Binomial expansions and Pascal's triangle Complete all the rows of Pascal's triangle forn = 0, 1, 2, 3, .. . , 12. Keep this in a prominent place for use in the rest of this chapter. ni nol o FOUNDATIO Exercise 15A %3D . Using Pascal's triangle to provide the binomial coefficients, give the expansions of: a (1 + x)6 b (1 – x)6 C ( 1 + x) d (1 - x)° e (1 + c)5 f (1+ 2y)* h (1 – 3z) (1-)* 8 (1 +)* 5 lo sulsk (1+ (1 + 3x\4 ontinue the calculations of the expansions of (1 + x)" at the beginning of this section, expanding + x)' and (1 + x)° in the same manner. Keep your work in columns, so that the addition prope Pascal's triangle is clear. the specified term in each expansion. gcbonqour of i ind the term in x', or (1 + x)": b For (1 - x)': where 0 in x?, find the term in x°. find the term ii find the term in r5
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