Question

prove that (a^-1+b^-1)^-1=ab/a+b​

Answer 1

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Step-by-step explanation:

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Asked on December 20, 2019 by

Raftaar Yarramsetti

Let x=1+a+a

2

+..... and y=1+b+b

2

.... where ∣a∣<1 and ∣b∣<1. Prove that 1+ab+a

2

b

2

+....=

x+y−1

xy

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ANSWER

Using C,P, we get

x=1+a+a

2

+......

x=

1−a

1

y=1+b+b

2

+......

y=

1−b

1

and Let P=1+ab+a

2

b

2

+......

P=

1−ab

1

and

x+y−1

xy

=

1−a

1

+

1−b

1

−1

1−a

1

×

1−b

1

x+y−1

xy

=

1−b+1−a−1+a+b−ab

1

=

1−ab

1

Since P=

1−ab

1

=

x+y−1

xy

Hence Proved.