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Problems
Contests
Undergraduate contests
VTRMC
1980 VTRMC
2
2
Part of
1980 VTRMC
Problems
(1)
1980 VTRMC #2
Source:
8/11/2020
The sum of the first
n
n
n
terms of the sequence
1
,
1
+
2
,
1
+
2
+
2
2
,
…
,
1
+
2
+
⋯
+
2
k
−
1
,
…
1,1+2,1+2+2^2,\ldots,1+2+\cdots+2^{k-1},\ldots
1
,
1
+
2
,
1
+
2
+
2
2
,
…
,
1
+
2
+
⋯
+
2
k
−
1
,
…
is of the form
2
n
+
R
+
S
n
2
+
T
n
+
U
2^{n+R}+Sn^2+Tn+U
2
n
+
R
+
S
n
2
+
T
n
+
U
for all
n
>
0.
n>0.
n
>
0.
Find
R
,
S
,
T
,
R,S,T,
R
,
S
,
T
,
and
U
.
U.
U
.