Question

一道数学题边长为1+√2,1+2√2,1+3√2,1+4√2的正方形的面积记作S1、S2、S3、S4、1.分别计算S2-

Answer 1

1、

S2-S1=(1+2√2)²-(1+√2)²

=1+4√2+8-1-2√2-2

=2√2+6

=2(√2+3)

S3-S2=(1+3√2)²-(1+2√2)²

=1+6√2+18-1-4√2-8

=2√2+10

=2(√2+5)

S1-S3==(1+4√2)²-(1+3√2)²

=1+8√2+32-1-6√2-18

=2√2+14

=2(√2+7)

2、Sn+1-Sn=(1+(n+1)√2)²-(1+n√2)²

=1+2(n+1)√2+2(n+1)²-1-2n√2-2n²

=2√2+2(2n+1)

=2(√2+2n+1)