the remainder when 1+x+x^2+....+x^1007 is divided by (x-1) is
Answers
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3
1
+
x
+
x
2
+
⋯
+
x
2006
=
x
2007
−
1
x
−
1
=
q
(
x
)
(
x
−
1
)
+
C
or
x
2007
−
1
=
q
(
x
)
(
x
−
1
)
2
+
C
(
x
−
1
)
now deriving both sides
2007
x
2006
=
2
q
(
x
)
(
x
−
1
)
+
q
'
(
x
)
(
x
−
1
)
2
+
C
Making now
x
=
1
we have
2007
=
C
so the answer is
2007..
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