1/2+【1/3+2/3】+【1/4+2/4+3/4】+...+【1/50+2/50+...+49/50】
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/27 23:54:11
![1/2+【1/3+2/3】+【1/4+2/4+3/4】+...+【1/50+2/50+...+49/50】](/uploads/image/z/8854835-59-5.jpg?t=1%2F2%2B%E3%80%901%2F3%2B2%2F3%E3%80%91%2B%E3%80%901%2F4%2B2%2F4%2B3%2F4%E3%80%91%2B...%2B%E3%80%901%2F50%2B2%2F50%2B...%2B49%2F50%E3%80%91)
xRn@~(Rxo]:SHH
(j9!J[߄=k
*EZ3|N;~1OˌcupQE
FXm-vګRSLiͷ.zrc>~F|cه?aXrMӓFri>%rh"Zf\+6*
_T$
$j.ծ8qKT$3d5~p~㧟?
+QutxV2NޕN65EjdLsѐyXx5>%a} [ ,xsYwMlsQ^!$28nfHID/~f^)]k-JIo$n >HGXB"[Ipo{)=IC`!c
&
mli ƭ-Ůpɼ shR&G2 %zA-_{
1/2+【1/3+2/3】+【1/4+2/4+3/4】+...+【1/50+2/50+...+49/50】
1/2+【1/3+2/3】+【1/4+2/4+3/4】+...+【1/50+2/50+...+49/50】
1/2+【1/3+2/3】+【1/4+2/4+3/4】+...+【1/50+2/50+...+49/50】
每一项的通项为n/2,是一个公差为1/2的等差数列.可用等差数列求和公式.
Sn=na1+n(n-1)d/2
=49×(1/2)+49×48×(1/4)
=612.5
或
Sn=(a1+an)n/2
=(1/2+49/2)×49/2
=612.5
1/2+【1/3+2/3】+【1/4+2/4+3/4】+...+【1/50+2/50+...+49/50】
=1/2+2/2+3/2+……+49/2
=(1/2+49/2)×49÷2
=25×49÷2
=612.5
该数列的通式为 (1+2+3+……+n)/(n+1)=n/2;
1/2+【1/3+2/3】+【1/4+2/4+3/4】+...+【1/50+2/50+...+49/50】共有49项
因此其和为 (1+49)*49/4=1225/2