Evaluate:
5*[25^n+1] - 25 * (5^2n) / 5 * (5^2n+3) - (25^n+1)
Answers
Answer:
The simplified answer is \frac{1}{6}
6
1
Step-by-step explanation:
\begin{gathered}\frac{5\times 25^{n+1}-25\times5^{2n} }{5\times 5^{2n+3}-25^{n+1} }\\\\=\frac{5\times 5^{2(n+1)}-25\times5^{2n} }{5\times 5^{2n+3}-5^{2(n+1)} }\\\\=\frac{5\times 5^{2n+2}-25\times5^{2n} }{5\times 5^{2n+3}-5^{2n+2} }\\\\=\frac{5\times 5^{2n}\times 5^{2} -25\times5^{2n} }{5\times 5^{2n}\times5^{3} -5^{2n}\times5^{2} }\end{gathered}
5×5
2n+3
−25
n+1
5×25
n+1
−25×5
2n
=
5×5
2n+3
−5
2(n+1)
5×5
2(n+1)
−25×5
2n
=
5×5
2n+3
−5
2n+2
5×5
2n+2
−25×5
2n
=
5×5
2n
×5
3
−5
2n
×5
2
5×5
2n
×5
2
−25×5
2n
Taking the common factor from both numerator and denominator
\begin{gathered}=\frac{5^{2n}\times 5^{2} (5-1)}{5^{2n}\times5^{2} (5^{2} -1 }\\\end{gathered}
=
5
2n
×5
2
(5
2
−1
5
2n
×5
2
(5−1)
Cancel out the common term from numerator and denominator.
\begin{gathered}=\frac{ (5-1)}{ (5^{2} -1 ) }\\\\=\frac{4}{25-1} \\\\=\frac{4}{24} \\\\=\frac{1}{6}\end{gathered}
=
(5
2
−1)
(5−1)
=
25−1
4
=
24
4
=
6
1
Step-by-step explanation:
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