3、明显 x=0 时,左右两边都为 0,
x=π 时,左边为 1,右边为 0,
所以区间为 [0,π)。
选 B
x+(1/3)x^3+(1/5)x^5+...= (1/2)ln[(1+x)/(1-x)]
∑(n:1->∞) 1/[(2n-1).9^n ] = ?
Solution :
x+(1/3)x^3+(1/5)x^5+...= (1/2)ln[(1+x)/(1-x)]
x=1/3
∑(n:1->∞) 1/[(2n-1).3^(2n-1) ]
= (1/2)ln[(1+1/3)/(1-1/3)]
=(1/2)ln2
∑(n:1->∞) 1/[(2n-1).9^n ]
=(1/3) ∑(n:1->∞) 1/[(2n-1).3^(2n-1) ]
=(1/3)(1/2)ln2
=(1/6)ln2