Question

It's urgent please give answer to this question

Answer 1

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!}}}$
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Here is your answer.
a1 = 1/2

a2 = 1/2 + 1/4

a3 = 1/2 + 1/4 + 1/8

an = 1/2 + 1/4 + --------. + 1/2^n

Hence
$a_{1} = 1 - \frac{1}{2} \\ \\ a _{2} = 1 - \frac{1}{4 } = 1 - \frac{1}{ {2}^{2} } \\ \\ a _{3} = 1 - \frac{1}{8} = 1 - \frac{1}{ {2}^{3} } \\ . \\ . \\ . \\ a_{n} = 1 - \frac{1}{ {2}^{n} }$
Therefore

$a _{n} = 1 - \frac{1}{ {2}^{n} }$
$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope \: it \: helps\: you}}}}}}}}}}}}}}}$

$\huge\boxed{\texttt{\fcolorbox{Red}{yellow}{Be brainly!!}}}$

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Answer 2

Hello Friend

Here is the answer.

$a_{1} = \frac{1}{2} \\ \\ a _{2} = \frac{1}{2} + \frac{1}{4} \\ \\ a_{3} = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} \\ \\ a_{n} = \frac{1}{2} + \frac{1}{4} + ............ + \frac{1}{2} {}^{n}$

So,

$a_{1} = 1 - \frac{1}{2} \\ \\ a_{2} = 1 - \frac{1}{4} \\ \: \: \: \: \: \: = 1 - \frac{1}{ {2}^{2} } \\ \\ a _{3} = 1 - \frac{1}{8} \\ \: \: \: \: \: \: = 1 - \frac{1}{ {2}^{3} } \\ \\ . \\ . \\ . \\ . \\ . \\ . \\ \\ a_{n} = 1 - \frac{1}{ {2}^{n} }$
Therefore,

$a_{n} = 1 - \frac{1}{ {2}^{n} }$

Hope it helps you.

@MSD