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Find each sum. $$9486+9479+9472+7465+\ldots+8919+8912$$

For this question we need to add and then check our answer by using estimation. So we know that when we add, we start on our right column and we moved towards our left. So we're going to start, are adding by using this far right column. So we have six plus four plus one gives us 11. We're going to drop our one and then carry our other one. Now we have one plus nine plus seven plus tree equals 20. So we want to drop. Are zero carry over our two. Next we have two plus one was zero plus five. This gives us eight. We have no need to carry over any numbers. Next, we have four plus seven plus eight. This gives us 19 so we drop our one Sorry. Drop. Our nine carry are one. Now I have one plus two plus nine gives us 12. Drop are two KR one and last. We have one plus two, which equals to read. So this is going to be our final answer when we add and that we need Teoh Estimate Teoh complete our second part of our problem. So when we look at 329,801 we should, after using estimation, get a number that's roughly equal to 300,000. So let's see what we end up getting. It's over 224,000 196. We would round this down into 200,000 because this, too, is less than, um, less than five sweet around everything Down. Next we have 7074. This would also ground down to just 7000. Then we have 98 1005 131. So this one we would around this to 99 are not 99 around this to 100,000. So now we add these up 000 zero. Post 70 is 700 in three plus one. So are estimated answer. Here is 307,000 which is in between our actual answer and the estimated answer. So this would be a good number to use for restoration

Here. We want to use the calculator to finding sums. When we use a calculator, we get 648 1070 Let's add in our columns and that's our answer.

So for this question, we have to calculate the following sons of and first you have every right to sounds, actually as a sub rather than using summation notation. Um, and then you can just add so your egg. If we ever rewrite this sounds, we have the summation. And this time you know that we start with three, which is the number of the bottom memory and before so this time is actually just have tutors. Um, and we're basically that plug in three and four and you were J. It's so we do not weak at this is sequences side of rape. I over too less sign of four isn't out thinking about the unit circle side of three. Pirate, too isn't equal since Magnet one and sign of four Piper June. She's saving us side of two pi of his equal zero. So you get negative one plus zero and that equals negative one. That's the result for our first son. For the second son, we do the same thing. And now this time we're going from 3 to 5 and our general formula is one over came by this one. So are some isn't a look like one over three, minus one plus one over four. What it's like plus one over five minus one. If we subtract you, should these we get 1/2 plus 1/3. That's one for you. Uh, so we obviously other we could right these in the denominator 12. So we get six over 12 plus or over phone us three over fall, and we have that get 13 number 12. So that is our answer for the second son on the deferred. Some began drinking very similar. We're playing into our general formula, but this time we're starting with zero in. And he looked too. Really? Get three to the zero minus one. Howard was 3221 minus one. Power plus re. She the two lightest hard. That's equal to three to the night. You first, us three she zero power us breathe in the first hour was just three. Um, it's an actual actually by the sub three mega first hours. 1/3 uh, three to use your powers. One that, plus one. And you're free as this is equal to 1 30 plus four. Um, And to add that we can give for a centimeter of three. Do you have one very plus 12 carrots? And you get that This is equal to 13. Well, Rick Zach, the answer for you.

Hello students in this problem we have to find us some of this series containing 15 terms. So the first time of the cities can be written as three by five. If I multiply 10 in both the numerator and denominator. Similarly, the second term can be written as 33 upon 55. If I multiply 100 In each numerator and denominator. Similarly. Similarly, the third time would be 333 up 1555 And the pattern goes on till 15 terms. So Taking three x 5 common here I get one again taking three by 45 common from the second number, I will get 11 upon 11 from the third number I will get 111 upon 111. And again this pattern is going to be continued till 15 times. So this is three x 5 times three x 5 times one plus 11 upon 11 is canceled. And this is equal to one again, this is going to be cancelled and equal to one. So one plus one plus one. This is going to be edited 15 number of times, So we get three x five, multiplied by 15 And this is 3-5, Sorry, three into 3, And the answer would be nine. That is the second choice. Thank you.