1. (8*100^n)/(2^(2*n+1)*5^(2*n-2))2. (5^(n+1) - 5^(n-1))/(2*5^n)3....

Question

1. (8*100^n)/(2^(2*n+1)*5^(2*n-2))
2. (5^(n+1) - 5^(n-1))/(2*5^n)
3. (a-sqrt(a)-2)/(2-sqrt(a))

Answer 1

8*100^n/2^n+1 * 5^n-2=2³*2^2n*5^2n/2^n+1 * 5^n-2=2^2n+3*5^2n/2^n+1 * 5^n-2=
=2²*5²=10²=100
2)(5^n+1  -5^n-1)/2*5^n=5^n-1 *(25-1)/2*5^n=5^n-1  *24/2*5^n=12/5=2,4
3)(a-√a-2)/(2-√a)=(a-√a-2)(2+√a)/(2-√a)(2+√a)=(2a+a√a-2√a-a-4-2√a)/(4-a)=
(a+a√a-4√a-4)/(4-a)=[a(1+√a)-4(√a+1)]/(4-a)=(a-4)(1+√a)/(4-a)=-1-√a