AP2 =( 1- 1/2+ 1/4)a

AP3 =( 1- 1/2+ 1/4- 1/8)a

AP4 =( 1- 1/2+ 1/4- 1/8+ 1/ 16)a

suppose

b 1=a

b2=(- 1/2)a

b3=( 1/4)a

b4=(- 1/8)a

...

AP 1 = b 1+B2 =( 1/2)a

AP2=b 1+b2+b3=(3/4)a

AP3=b 1+b2+b3+b4=(5/8)a

B 1, b2, b3 is a geometric series, which can be obtained by the summation formula of equal ratio series.

apn=sb(n+ 1)=a[ 1-(- 1/2)^(n+ 1)]/[ 1-(- 1/2)]

=(2/3)a[ 1+(- 1)^n/ 2^(n+ 1)]