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Komok [63]
3 years ago
13

This is exact and approximate piSOMEONE PLS HELP BEFORE I FAIL​

Mathematics
1 answer:
Kisachek [45]3 years ago
3 0
3.14159 this is pi followed by 2653589 circumference over diameter 79323 OMG can’t you see 8462643 and now we’re on a spree 38 and 32 now we’re blue, oh, who knew 7 thousand 9 hundred 50 and then a 2 88 and 41 so much fun now we run 97169399 then 3751 half-way done 458 now don’t be late 2 oh 9 where’s the wine 74 it’s on the floor then 94459 23 oh we gotta go 78 we can’t wait 164 oh 628 we’re almost near the end keep going 62 we’re getting through oh 899 on time 8628 oh 34 there’s only a few more 82 then 53 42117 oh and 67 we’re done, was that fun? Learning random digits so you can brag to your friends


That was the 100 digits of pi, your welcome
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Answer:

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Step-by-step explanation:

If you expand the series, you can see the first few terms of the series:

  • Putting 1 in n, \frac{1}{2}(1)-\frac{1}{2}=0
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We can see the series is 0, 0.5, 1, 1.5, ....

This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.

We know formula for sum of arithmetic series:

s_{n}=\frac{n}{2}(2a+(n-1)d)

Where,

  • S_{n} denotes the nth partial sum
  • a is the first term (in our case it is 0)
  • n is the term (in our case it is 10 since we want to find 10th partial sum -- sum until first 10 terms)
  • d is the common difference (difference in term and the previous term) (in our case it is 0.5)

Substituting these into the formula, we get the 10th partial sum to be:

s_{10}=\frac{10}{2}(2(0)+(10-1)(0.5))\\s_{10}=5(0+(9)(0.5))\\s_{10}=5(0+4.5)\\s_{10}=5(4.5)\\s_{10}=22.5

So the sum of the first 10 terms is 22.5. Third answer choice is right.


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