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观察下列各式:(x2%1)÷(x%1)=x+1(x3%1)÷(x%...

根据上面的式子可得:1+x+x2+x3+…+xn=(xn+1-1)÷(x-1),∴1+2+22+…+262+263=(263+1-1)÷(2-1)=264-1.故填:264-1.

(1)∵(x2-1)÷(x-1)=x+1,(x3-1)÷(x-1)=x2+x+1,(x4-1)÷(x-1)=x3+x2+x+1,(x5-1)÷(x-1)=x4+x3+x2+x+1,∴(xn-1)÷(x-1)=xn-1+xn-2+…+1,∴(x6-1)÷(x-1)=x5+x4+x3+x2+x+1;(2)∵(x6-1)÷(x-1)=x5+x4+x3+x2+x+1,∴x6-1=...

(1)∵(x2-1)÷(x-1)=x+1(x3-1)÷(x-1)=x2+x+1(x4-1)÷(x-1)=x3+x2+x+1(x5-1)÷(x-1)=x4+x3+x2+x+1…∴(xn-1)÷(x-1)=xn-1+…+x3+x2+x+1;故答案为:xn-1+…+x3+x2+x+1;(2)1+2+22+23+…+214+215=(216-1)÷(2-1)=216-1.故答案为...

(1)(xn-1)÷(x-1)=xn-1+xn-2+…+x+1;(2)1+2+22+23+…+262+263=(264-1)÷(2-1)=264-1.故答案是xn-1+xn-2+…+x+1;264-1.

(1)根据各式的规律可得:(x-1)(xn+xn-1+…+x2+x+1)=xn+1-1;(2)根据各式的规律得:1+2+22+23+…+262+263=(2-1)(263+262+…+23+22+2+1)=264-1,∵21=2,22=4,23=8,24=16,25=32,…,且64÷4=16,∴264个位上数字为6,则1+2+22+23+…+262+2...

解: 根据题意得 (x^n-1)/(x-1)=x^(n-1)+x^(n-2)+……+x+1 1+2+2^2+2^3+…2^62+2^63 =(2^64-1)/(2-1) =2^64-1

(1)(x-1)(x+1)=x2-1;(x-1)(x2+x+1)=x3-1;(x-1)(x3+x2+x+1)=x4-1;(2)(x-1)(x5+x4+x3+x2+x+1)=x6-1;(3)利用你发现的规律计算:(x-1)(x6+x5+x4+x3+x2+x+1)=x7-1;(4)1+4+42+43+…+42013=13×(4-1)×(1+4+42+43+…+4...

原式=(x-1)÷ 2-x-1 x+1 =(x-1)÷ 1-x x+1 =(x-1)× x+1 1-x =-x-1.由x为方程x 2 +3x+2=0的根,解得x=-1或x=-2.当x=-1时,原式无意义,所以x=-1舍去;当x=-2时,原式=-(-2)-1=2-1=1.

x²-x-1=0 x²-x=1 x²-x+1/4=1+1/4 (x-1/2)²=5/4 x-1/2=±√5/2 x=1/2±√5/2=(1±√5)/2 x²=(1±2√5+5)/2=(6±2√5)/2=3±√5 x³=(1±3√5+15±5√5)/8=(16±8√5)/8=2±√5 (1-3/x+2)÷x-1/x²+2x-x/x+1 =(3-3/x)÷x-1/x²+2...

(1)x2-1=(x-1)(x+1),∴x2?1x+1=x-1;(2)x3-1=(x-1)(x2+x+1),∴x3?1x2+x+1=x-1;(3)x4-1=(x-1)(x3+x2+x+1),∴x4?1x3+x2+x+1=x?1;(4)猜想:xn-1=(x-1)(xn-1+xn-2+…+x+1),∴xn?1xn?1+xn?2+…+x+1=x-1;当n=11,x11-1=(x-...

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