Question

Prove that 2^30+2^29+2^28/2^31+2^30+2^28 =1/2

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

LHS

=

2

31

+2

30

−2

29

2

30

+2

29

+2

28

=

2

29+2

+2

29+1

−2

29

2

28+2

+2

28+1

+2

28

Applying a

m+n

=a

m

×a

n

:

=

2

29

×2

2

+2

29

×2

1

−2

29

2

28

×2

2

+2

28

×2

1

+2

28

Factor out x

28

from numerator and x

29

from denominator:

=

2

29

(2

2

+2

1

−1)

2

28

(2

2

+2

1

+1)

Simplify further:

=

2(4+2−1)

4+2+1

=

2(5)

7

\begin{lgathered}= \frac{7}{10}\\ \\ \text{=RHS (Proved)}\end{lgathered}

=

10

7

=RHS (Proved)