What is $1+4(1/2)+6(1/2)^2+4(1/2)^3+1(1/2)^4$ ? More specifically, what is the "quick" way to solve this?

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I believe there is a quick way for this. I just can't remember it right now.

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Answer 1 · 2017-12-15T21:12:05

$5.0625$

Pascal's triangle:

$1$
$1 1$
$1 2 1$
$1 3 3 1$
$1 4 6 4 1$

the fourth row, with $1 4 6 4 1$ , is used for binomials to the power of $4$ .

the two terms in the binomial expression are $1$ and $1/2$ .

$(1+1/2)^4 = 1^4*1 + 4*1^3*(1/2) + 6*1^2*(1/2)^2 + 4*1^1(1/2)^3 + 1(1/2)^4$

$(1+1/2)^4 = (1 1/2) ^4$

$= 1.5^4$

$=5.0625$