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Question 0502e
Sigma Notation
Change of Variable
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It is given that
∑
r
=
3
n
1
r
(
r
+
1
)
=
1
3
−
1
n
+
1
.
\sum_{r=3}^n \frac{1}{r(r+1)} = \frac{1}{3} - \frac{1}{n+1}.
r
=
3
∑
n
r
(
r
+
1
)
1
=
3
1
−
n
+
1
1
.
Find an expression for
∑
r
=
3
n
1
(
r
+
2
)
(
r
+
3
)
\displaystyle \sum_{r=3}^{n} \frac{1}{(r + 2)(r + 3)}
r
=
3
∑
n
(
r
+
2
)
(
r
+
3
)
1
in term form
A
−
1
n
+
B
,
{\displaystyle A - \frac{1}{n+B},}
A
−
n
+
B
1
,
where
A
{A}
A
and
B
{B}
B
are constants to be determined.
Attempt
A
=
{A = }
A
=
B
=
{B = }
B
=
Answer
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