Answer:
∑
i=1
(
−
1
)
i
+
1
⋅
5
⋅
2
i
−
1
Explanation:
∑
=
5
−
10
+
20
−
40
+
80
−
...
.
.
Here we have a sequence of terms with alternating sign beginning positive.
To achieve this we need a term
(
−
1
)
1
+
1
for
i
from
1
→
n
Only considering the absolute values of the terms, we have sequence where
a
n
=
2
⋅
a
n-1
and
a
1
=
5
To achieve this we need a term
5
⋅
2
i
−
1
for
i
from
1
→
n
Combining these results we have our sum in sigma notation:
n
∑
i=1
(
−
1
)
i
+
1
⋅
5
⋅
2
i
−
1
