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MAA AMC
AMC 8
1993 AMC 8
19
Telescoping
Telescoping
Source: 1993 AMC 8 Problem 19
June 28, 2011
AMC
Problem Statement
(
1901
+
1902
+
1903
+
⋯
+
1993
)
−
(
101
+
102
+
103
+
⋯
+
193
)
=
(1901+1902+1903+\cdots + 1993) - (101+102+103+\cdots + 193) =
(
1901
+
1902
+
1903
+
⋯
+
1993
)
−
(
101
+
102
+
103
+
⋯
+
193
)
=
(A)
167
,
400
(B)
172
,
050
(C)
181
,
071
(D)
199
,
300
(E)
362
,
142
\text{(A)}\ 167,400 \qquad \text{(B)}\ 172,050 \qquad \text{(C)}\ 181,071 \qquad \text{(D)}\ 199,300 \qquad \text{(E)}\ 362,142
(A)
167
,
400
(B)
172
,
050
(C)
181
,
071
(D)
199
,
300
(E)
362
,
142
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