2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Summation by Sigma Method
If fx = 9x9...
Question
If
f
(
x
)
=
9
x
9
x
+
3
, then
f
(
1
2012
)
+
f
(
2
2012
)
+
.
.
.
.
+
f
(
2011
2012
)
is equal to
A
1005
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1005.5
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
1006
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1006.5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
B
1005.5
Given that
f
(
x
)
=
9
x
9
x
+
3
⇒
f
(
1
−
x
)
=
9
(
1
−
x
)
9
(
1
−
x
)
+
3
=
3
3
+
9
x
So we get
f
(
x
)
+
f
(
1
−
x
)
=
9
x
9
x
+
3
+
3
3
+
9
x
=
1
The given equation can be written as
y
=
f
(
1
2012
)
+
f
(
2
2012
)
+
.
.
.
.
.
.
.
+
f
(
2011
2012
)
=
f
(
1
2012
)
+
f
(
2
2012
)
+
.
.
.
.
.
+
f
(
1006
2012
)
+
.
.
.
.
+
f
(
1
−
2
2012
)
+
f
(
1
−
1
2012
)
⇒
y
=
f
(
1
2012
)
+
f
(
1
−
1
2012
)
+
f
(
2
2012
)
+
f
(
1
−
2
2012
)
.
.
.
.
.
+
f
(
1006
2012
)
⇒
y
=
1
+
1
+
1
+
.
.
.
.
.
.
(
1005
t
e
r
m
s
)
+
f
(
1
2
)
=
1005
+
0.5
=
1005.5
Suggest Corrections
0
Similar questions
Q.
if
f
(
x
)
=
9
x
9
x
+
3
then
f
(
1
1996
)
+
f
(
2
1996
)
+
.
.
.
.
.
.
.
.
.
Q.
lf
f
(
x
)
=
9
x
9
x
+
3
then
f
(
1
1996
)
+
f
(
2
1996
)
+
…
…
…
.
+
f
(
1995
1996
)
=
Q.
lim
x
→
0
sin
x
2012
−
x
2012
cos
x
2012
+
(
x
3
)
2012
x
2012
(
e
5.
x
2012
−
1
−
5.
x
2012
)
is equal to-
Q.
If
f
(
x
)
=
x
3
−
6
x
2
+
9
x
+
3
then
f
(
2
)
is equal to
Q.
Let
f
(
x
)
=
9
x
9
x
+
3
. Show
f
(
x
)
+
f
(
1
−
x
)
=
1
, and hence evaluate
f
(
1
1996
)
+
f
(
2
1996
)
+
f
(
3
1996
)
+
.
.
.
+
f
(
1995
1996
)
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Summation by Sigma Method
MATHEMATICS
Watch in App
Explore more
Summation by Sigma Method
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app