计算(1+1/3+1/5+1/7+1/9+1/11+1/13)×819,它的整数部分是_.
问题描述:
计算(1+
+1 3
+1 5
+1 7
+1 9
+1 11
)×819,它的整数部分是______. 1 13
答
(1+
+1 3
+1 5
+1 7
+1 9
+1 11
)×8191 13
=1×819+
×819+1 3
×819+1 7
×819+1 9
×819+1 13
×819+1 5
×819,1 11
=819+273+117+91+63+
+819 5
,819 11
=(819+273+117+91+63+163+74)+
+4 5
,5 11
=1600+
,69 55
=1601+
;14 55
所以,它的整数部分是1601.
故答案为:1601.