计算:(3+1)(32+1)(34+1)(38+1)−3162.

问题描述:

计算:

(3+1)(32+1)(34+1)(38+1)−316
2

分母=

1
2
(32-1)(32+1)(34+1)(38-1)-316
=
1
2
(34-1)(34+1)(38+1)-316
=
1
2
(38-1)(38+1)-316
=
1
2
(316-1)-316
=-
1
2
(316+1),
则原式=
1
2
(316+1)
2
=-
1
4
(316+1).