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Alina [70]
3 years ago
6

Help me please I am lost

Mathematics
1 answer:
goblinko [34]3 years ago
7 0

Answer:

The answer to your question is:

a)   f(a) -2 = a² - 3

b)    f(a - 2) = a² - 4a + 3

c)     f(b + d) = b² + 2bd + d² - 1

Step-by-step explanation:

a. f(a) - 2 = (a)² - 1 - 2

  f(a) -2 = a² - 3

b. f(a - 2) = (a - 2)² - 1

    f(a - 2) = a² - 4a + 4 - 1

    f(a - 2) = a² - 4a + 3

c. f(b + d) = (b + d)² - 1

   f(b + d) = b² + 2bd + d² - 1

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Step-by-step explanation:

<u><em>Step(i):-</em></u>

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Let   U_{n} = (-1)^{n} \frac{n^{2} }{n^{3}+3 }

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Uₙ-Uₙ₋₁ <0

<u><em>Step(ii):-</em></u>

    \lim_{n \to \infty} U_n =  \lim_{n \to \infty}\frac{n^{2} }{n^{3}+3 }

                       =  \lim_{n \to \infty}\frac{n^{2} }{n^{3}(1+\frac{3}{n^{3} } ) }

                    = =  \lim_{n \to \infty}\frac{1 }{n(1+\frac{3}{n^{3} } ) }

                       =\frac{1}{infinite }

                     =0

    \lim_{n \to \infty} U_n =0

∴ Given series is converges

                       

                     

 

3 0
3 years ago
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