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d1i1m1o1n [39]
3 years ago
15

The square root of a number is 2k. what is half of the number?​

Mathematics
1 answer:
hammer [34]3 years ago
8 0

2k isuwgqjaiqu2yquqi

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Find the sum of the convergent series. (round your answer to four decimal places. ) [infinity] (sin(9))n n = 1
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The sum of the convergent series \sum_{n=1}^{\infty}~(sin(1))^n is 5.31

For given question,

We have been given a series \sum_{n=1}^{\infty}~(sin(1))^n

\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n

We need to find the sum of given convergent series.

Given series is a geometric series with ratio r = sin(1)

The first term of the given geometric series is a_1=sin(1)

So, the sum is,

= \frac{a_1}{1-r}

= sin(1) / [1 - sin(1)]

This means, the series converges to sin(1) / [1 - sin(1)]

\sum_{n=1}^{\infty}~(sin(1))^n

= \frac{sin(1)}{1-sin(1)}

= \frac{0.8415}{1-0.8415}

= \frac{0.8415}{0.1585}

= 5.31

Therefore, the sum of the convergent series \sum_{n=1}^{\infty}~(sin(1))^n is 5.31

Learn more about the convergent series here:

brainly.com/question/15415793

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