Find the first 3 terms, in ascending powers of , of the binomial expansion of
giving each term in simplest form.
Use your answer to part (a) to estimate .
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Find the first 3 terms, in ascending powers of , of the binomial expansion of
giving each term in simplest form.
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Use your answer to part (a) to estimate .
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Expand
giving your answer in descending powers of .
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Expand
giving your answer in ascending powers of .
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Find, in simplest form, the coefficient of in the expansion of
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Without using a calculator, find the value of
(i)
(ii)
(iii)
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Find the coefficient of in the binomial expansion of
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Find, in simplest form, the coefficient of in the expansion of
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In the binomial expansion of
where
is a constant
the coefficient of is 15120
Find the value of a.
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In the binomial expansion of
the coefficient of is 12 976 128.
Find the value of .
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Find the first 3 terms, in ascending powers of , of the binomial expansion of
giving each term in simplest form.
How did you do?
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Find the first 3 terms, in ascending powers of , of the binomial expansion of
giving each term in simplest form.
How did you do?
Use your answer to part (a) to estimate the value of .
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Expand
giving your answer in descending powers of .
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In the binomial expansion of
where is a non-zero constant, the coefficient of
is twice the coefficient of
.
Find the value of , giving your answer as a simplified fraction.
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In the binomial expansion of
the coefficient of is 96.
Given that , find the value of
.
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Find the first 3 terms, in ascending powers of , of the binomial expansion of
giving each term in simplest form.
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Use your answer to part (a) to estimate .
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In the binomial expansion of
the coefficient of is equal to the coefficient of
.
Find the non-zero value of .
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In the binomial expansion of
the coefficient of is four times the coefficient of
.
Find the possible values of .
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Find the first 3 terms, in ascending powers of , of the binomial expansion of
giving each term in simplest form.
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Given that is small such that
and higher powers of
can be ignored show that
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In the binomial expansion of
where and
the coefficients of
and the coefficient of
are equal.
Find an expression for in terms of
.
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Find the coefficient of in the binomial expansion of
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Find the first 3 terms, in ascending powers of , of the binomial expansion of
giving each term in simplest form.
How did you do?
Use your answer to part (a) to estimate .
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Find the first 3 terms, in ascending powers of , of the binomial expansion of
giving each term in simplest form.
How did you do?
Given that is small such that
and higher powers of
can be ignored show that
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In the binomial expansion of
the coefficient of is 19 440.
Given that is a positive integer, find the value of
.
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Expand
giving your answer in ascending powers of .
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Expand
giving your answer in ascending powers of .
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Find the coefficient of in the expansion of
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In the binomial expansion of
the coefficient of is -10.
Find the possible values of .
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Find the first terms, in ascending powers of
, of the binomial expansion of
giving each term in simplest form.
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Find the coefficient of in the series expansion of
, giving your answer as a simplified fraction.
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where
is a constant
Given that one of the terms in the binomial expansion of is
find the value of .
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Using this value of ,
find the constant term in the expansion of
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In the binomial expansion of
the coefficient of is equal to the coefficient of
.
Find the non-zero value of .
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In the binomial expansion of
where and
the coefficient of
is equal to the coefficient of
.
Find in terms of
.
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In the binomial expansion of
the coefficient of is equal to the coefficient of
.
Find the value of
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Given that and
are integers, and that
, find the values of
and
.
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In the binomial expansion of the coefficient of
is 216.
In the binomial expansion of the coefficient of
is 4860.
Find the possible values of and
.
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Use the formula
to prove that
for all positive integer values of .
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In the binomial expansion of
the coefficient of is equal to the coefficient of
.
Find the values of , giving your answers in the form
where
and
are integers to be found.
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In the binomial expansion of
where and
, the coefficient of
is double the coefficient of
.
Find in terms of
.
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In the binomial expansion of the coefficient of
is -870 912.
In the binomial expansion of the coefficient of
is -1 557 135 360.
Find the possible values of and
.
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Given that
use algebra to show that satisfies the cubic equation
and hence write down the value of .
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In the binomial expansion of
the coefficient of is 84.
Find the value of .
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Use the first 3 terms, in ascending powers of , of the expansion of
to find an approximation for .
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Find the percentage error in the approximation from part (a) to the exact value of
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Given that represents a very small value, so that
(and higher powers of
) can be ignored, show that
where ,
and
are integers to be found.
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In the binomial expansion of
the coefficient of is -3240.
Find the value of .
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