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Mathematics
Mathematics
Problem
a
a
a
,
b
b
b
, and
c
c
c
are consecutive terms of an arithmetic sequence. Prove that the following are also consecutive terms of an arithmetic sequence: a.
b
+
c
b + c
b
+
c
,
c
+
a
c + a
c
+
a
, and
a
+
b
a + b
a
+
b
b.
1
b
+
c
\frac{1}{\sqrt{b} + \sqrt{c}}
b
+
c
1
,
1
c
+
a
\frac{1}{\sqrt{c} + \sqrt{a}}
c
+
a
1
, and
1
a
+
b
\frac{1}{\sqrt{a} + \sqrt{b}}
a
+
b
1
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