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Use binomial expansion to evaluate (1.02)^6 to 4 s. f

Use binomial expansion to evaluate (1.02)^6 to 4 s. f

Answers

Grace
Use pascals triangle to get the coefficient when n=6
You need to write 1.02 in form of a+b for instance (1+0.02) where a is 1 and b is 0.02.
In expansion of (1+0.02)^6, the terms without coefficients are as follows
1^6, 1^5(0.02)^1, 1^4(0.02)^2, 1^3(0.02)^3, 1^2(0.02)^4, 1^1(0.02)^5, 0.02^6
The coefficient for n=6 are
1,6,15,20,15,6,1
multiply terms with corresponding coefficient to get..
1+0.12+0.0060+0.00016+0.0000024+0.0000000192+0.000000000064
Since we only need an answer to 4sf, it is sufficient to consider adding up to the fourth term of this expansion.. you get
=1.12616
=1.126(4sf)
Gracemakena answered the question on September 28, 2017 at 07:37

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