What is 1/(2*2^{n-1)*{2(2^n-1)+(2^{n-1}-1)*2}} ?

The solution to 1/(2*2^{n-1)*{2(2^n-1)+(2^{n-1}-1)*2}} is 1/(2^n(2^n+2^{n+1)-4)}

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simplify 1/(22^{n-1){2(2^n-1)+(2^{n-1}-1)*2}}

simplify

\frac{1}{2 \cdot 2 ^{n - 1} \cdot { 2 ( 2 ^{n} - 1 ) + ( 2 ^{n - 1} - 1 ) \cdot 2 }}

\frac{1}{2 ^{n} ( 2 ^{n} + 2 ^{n + 1} - 4 )}

Solution steps

\frac{1}{2 \cdot 2 ^{n - 1} ( 2 ( 2 ^{n} - 1 ) + ( 2 ^{n - 1} - 1 ) \cdot 2 )}

Simplify

2 \cdot 2^{n - 1} : 2^{n}

= \frac{1}{2 ^{n} ( 2 ( 2 ^{n} - 1 ) + ( 2 ^{n - 1} - 1 ) \cdot 2 )}

Expand

2 (2^{n} - 1) + (2^{n - 1} - 1) \cdot 2 : 2^{n} + 2^{n + 1} - 4

= \frac{1}{2 ^{n} ( 2 ^{n} + 2 ^{n + 1} - 4 )}

\frac{- 21 y ^{3}}{- 3 y ^{2}}

(m^{c})^{1}

(x^{2} + 4 x + 3) (2 x^{2} - 9 x + 7)

\frac{1}{cos ^{2} ( x )} + \frac{1}{sin ^{2} ( x )}

\frac{( 1 + sin ( a ) )}{( 1 - sin ( a ) )}

What is 1/(2*2^{n-1)*{2(2^n-1)+(2^{n-1}-1)*2}} ?
The solution to 1/(2*2^{n-1)*{2(2^n-1)+(2^{n-1}-1)*2}} is 1/(2^n(2^n+2^{n+1)-4)}