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∑
k
=
0
1
(
2
−
k
)
=
\sum_{k=0}^{1}(2-k)=
∑
k
=
0
1
(
2
−
k
)
=
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Math Problems
Calculus
Find derivatives using the chain rule I
Full solution
Q.
∑
k
=
0
1
(
2
−
k
)
=
\sum_{k=0}^{1}(2-k)=
∑
k
=
0
1
(
2
−
k
)
=
Series Calculation:
The series is finite and only has two terms, for
k
=
0
k=0
k
=
0
and
k
=
1
k=1
k
=
1
. We will calculate each term separately.
Term for
k
=
0
k=0
k
=
0
:
For
k
=
0
k=0
k
=
0
, the term is
(
2
−
0
)
(2-0)
(
2
−
0
)
, which equals
2
2
2
.
Term for
k
=
1
k=1
k
=
1
:
For
k
=
1
k=1
k
=
1
, the term is
(
2
−
1
)
(2-1)
(
2
−
1
)
, which equals
1
1
1
.
Sum of Terms:
Now, we add the two terms together:
2
+
1
=
3
2 + 1 = 3
2
+
1
=
3
.
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