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Mathematics
Mathematics
Problem
If
α
\alpha
α
,
β
\beta
β
are natural numbers such that
100
α
−
199
β
=
(
100
)
(
100
)
+
(
99
)
(
101
)
+
(
98
)
(
102
)
+
⋯
+
(
1
)
(
199
)
100^\alpha - 199\beta = (100)(100) + (99)(101) + (98)(102) + \dots + (1)(199)
10
0
α
−
199
β
=
(
100
)
(
100
)
+
(
99
)
(
101
)
+
(
98
)
(
102
)
+
⋯
+
(
1
)
(
199
)
, then the slope of the line passing through
(
α
,
β
)
(\alpha, \beta)
(
α
,
β
)
and origin is (a) 530 (b) 510 (c) 550 (d) 540
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