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# HELP !! C2 QUESTION ON SERIES AND SEQUENCES - binomial expansion watch

1. HEY :P
a )Expand (1 + 2X)^10 in ascending powers of x up to and including the term in x^3
, simplifying
each coefficient.

ANSWER : 1 + 5x + (45/4X)^2 + 15X^3 +....

b) By substituting a suitable value of x into your answer for part a, obtain an estimate for
i 1.00510 ii 0.99610

I'm confused as to how to solve part b are we to just guess and use trial and error which number would give a close enough number to what they are asking for ,or is there a way to actually solve it ?

thank you , would appreciate the help
2. I think you do 1 + 2X = 1.0051 and solve for X, then substitute that value into your expansion for an approximation (so X would be 0.00255 in this case)
HEY :P
a )Expand (1 + 2X)^10 in ascending powers of x up to and including the term in x^3
, simplifying
each coefficient.

ANSWER : 1 + 5x + (45/4X)^2 + 15X^3 +....

b) By substituting a suitable value of x into your answer for part a, obtain an estimate for
i 1.00510 ii 0.99610

I'm confused as to how to solve part b are we to just guess and use trial and error which number would give a close enough number to what they are asking for ,or is there a way to actually solve it ?

thank you , would appreciate the help
Your expansion is valid for therefore we must get .

If we wish to approximate then we can say and hence which is indeed in our range.

So we can just sub that into the expansion.
4. (Original post by RDKGames)
Your expansion is valid for therefore we must get .

If we wish to approximate then we can say and hence which is indeed in our range.

So we can just sub that into the expansion.
thank you so much
5. (Original post by MathsPhysMind)
I think you do 1 + 2X = 1.0051 and solve for X, then substitute that value into your expansion for an approximation (so X would be 0.00255 in this case)
thank you
HEY :P
a )Expand (1 + 2X)^10 in ascending powers of x up to and including the term in x^3
, simplifying
each coefficient.

ANSWER : 1 + 5x + (45/4X)^2 + 15X^3 +....
This is an expansion of (1 + x/2)^10 rather than of (1 + 2x)^10.

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Updated: March 13, 2018
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