I need someone to find a mistake in my soliution or maybe to solf it much more easily... I have got a sum
1+
1
4⋅
2
4
+
1
7⋅
2
7
+
1
10⋅
2
10
+⋯
1+14⋅24+17⋅27+110⋅210+⋯
and need to evaluate it. So here's my soliution:
S(x)=1+
x
4
4⋅
2
4
+
x
7
7⋅
2
7
+
x
10
10⋅
2
10
+⋯=1+
∑
n=1
∞
x
3n+1
(3n+1)⋅
2
3n+1
=1+
S
1
(x)
