 | ■No25789に返信(高校２年さんの記事)
> 初項から第８項までの和が２、第１６項までの和が８のとき、第２４項までの和はなにか
In[35]:=
Solve[{Sum[r^k*a[1], {k, 1, 8}] == 2,
Sum[r^k*a[1], {k, 1, 16}] == 8},
{a[1], r}]
Out[35]=
{{a[1] -> 1/3*(3 - 3^(7/8)), r -> 3^(1/8)},
{a[1] -> 1/3*(3 - I*3^(7/8)),
r -> -I*3^(1/8)},
{a[1] -> 1/3*(3 + I*3^(7/8)),
r -> I*3^(1/8)},
{a[1] -> 1/3*(3 + 3^(7/8)),
r -> -3^(1/8)},
{a[1] -> 1/3*(3 - (-1)^(1/4)*3^(7/8)),
r -> -(-1)^(3/4)*3^(1/8)},
{a[1] -> 1/3*(3 + (-1)^(1/4)*3^(7/8)),
r -> (-1)^(3/4)*3^(1/8)},
{a[1] -> 1/3*(3 - (-1)^(3/4)*3^(7/8)),
r -> -(-1)^(1/4)*3^(1/8)},
{a[1] -> 1/3*(3 + (-1)^(3/4)*3^(7/8)),
r -> (-1)^(1/4)*3^(1/8)}}
(*かってに N-----a---->a[n]∈R と 解釈し；
In[36]:=
Simplify[Sum[r^k*a[1], {k, 1, 24}] /.
{a[1] -> 1/3*(3 - 3^(7/8)),
r -> 3^(1/8)}]
Out[36]=
26
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