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#