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Helen [10]
3 years ago
10

50 POINTS FOR 5 QUESTIONS, THEY SHOULD BE PRETTY EASY IF UR PAST 7TH GRADE. ANSWER QUICKLY PLEASE AND I'LL BE DONE FOR THE DAY T

HANKSSSSSSSSSSSSSSSSSSSS

Mathematics
1 answer:
antoniya [11.8K]3 years ago
3 0
P>4
t>4
r>2
for the 4th picture
1 matches with #2
2 matches with #1
4 matches with #3
3 matches with #4
for the 5th picture
3 matches with #1
2 matches with #2
4 matches with #3
1 matches with #4
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Alexus [3.1K]

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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