Question

数学问题:写出此数列的通项公式:1/2,1/4,-5/8,13/16,-29/32,61/64...

Answer 1

分母2^n

分子-(2-3),4-3,-(8-3),16-3,-(32-3),64-3

即(2-3)(-1),(2^2-3)(-1)^2,(2^3-3)(-1)^3,(2^4-3)(-1)^4,(2^5-3)(-1)^5,(2^6-3)(-1)^6

即(2^n-3)(-1)^n

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

=(2^n-3)/(-2)^n