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alisha [4.7K]
2 years ago
6

Prove usin's Mathematical induction 2^n ≤(n+1)!, for n≥0​

Mathematics
1 answer:
Westkost [7]2 years ago
8 0

Answer:

Step-by-step explanation:

2^0 is less than or equal to 1!, because 1<= 1

if 2^n <= (n+1)!, we wish to show that 2^(n+1) <= (n+2)!, since

(n+2)! = (n+1)! * (n+2), and (n+1)!>= 2^n, then we want to prove that n+2<=2, which is always true for n>=0

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Nitella [24]

Answer:

#3: x is approximately 0.37, -5.37, #4: x is approximately 4.19, -1.19

Step-by-step explanation:

You can solve using the quadratic equation or by solving with the perfect square

\frac{-b+/-\sqrt{b^{2}-4ac} }{2a} = x^{2}+5x-2=0\\ \frac{-5+/-\sqrt{5^{2}-4(1)(-2) }}{2(1)}

x is approximately 0.37, -5.37

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3 years ago
I have 8 questions witch means 80 points answer correctly!
kolezko [41]
<h3>Answer : </h3>

\Large \pink{\tt \dfrac{35}{36}}

<h3>Solution :</h3>

\tt \dfrac{3}{4} + \dfrac{2}{9}

By taking LCM = 4 × 9 = 36

\tt = \dfrac{3 \times 9}{4 \times 9} + \dfrac{2 \times 4}{9 \times 4}

\tt = \dfrac{27}{36} + \dfrac{8}{36}

\tt = \dfrac{27 + 8}{36}

\tt = \dfrac{35}{36}

\pink{\tt \therefore \: Answer \: is \: \dfrac{35}{36}}

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3 years ago
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zysi [14]

Answer:


Step-by-step explanation:

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