Question

求一数学题，答案请详细

若f(x)=1/(2的X次方-1) +a是奇函数，则A=

Answer 1

f(-x)=-f(x)
f(-x)+f(x)=0
1/(2^x-1)+a+1/(2^-x-1)+a=0
后面上下乘2^x
1/(2^x-1)+2^x/(1-2^x)+2a=0
1/(2^x-1)-2^x/(2^x-1)+2a=0
所以-(2^x-1)/(2^x-1)+2a=0
-1+2a=0
a=1/2

Answer 2

令a=1/2+1/3+...+1/99
原式=(1+a)(a+1/100)-a(1+a+1/100)
=a(1+a)+1/100(1+a)-a(1+a)-1/100a
=1/100(1+a)-1/100a
=1/100+1/100a-1/100a
=1/100