1/4+1/16+1/64+.+1/4n次方=

Question

1/4+1/16+1/64+.+1/4n次方=

Answer 1

令S(n)=1/4+1/16+1/64+.+1/4n次方 (1)
两边乘以4 4S(n)=1+1/4+1/16+1/64+.+1/4^n-1次方 (2)
(2)-(1) 得
3S(n)=1-1/4^n次方
S(n)=1/3-1/3*4^n次方