What is the sum of the infinite geometric series 1 - 1/2 + 1/4 - 1/8 + 1/16
1 answer:
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<h3><u>Solution</u><u>:</u></h3>
Please find the photograph for the square root of 3.
- Firstly, you have to write 3 as 3. 00 00 00.
- Then we should find out the root of the perfect square which is less than 3. Here, 1 is the required perfect square root because 1 × 1 = 1 only which is less than 3.
- Now 3 - 1 = 2 and we are placing 2 zeros after it so that it will be 200. Now we have to add 1 with the divisor 1 which will be 2. Then we have to select a number to be placed beside this 2 in such a way that if we multiply this combined number with the new number, then we will get a number which is less than 200. We see that if we place 7 after 2 and multiply 27 with 7, we get 189 which is less than 200.
- Now 200 - 189 = 11 and we are placing 2 zeros after it so that it will be 1100. Now we have to add 7 with the divisor 27 which will be 34. Then we have to select a number to be placed beside this 34 in such a way that if we multiply this combined number with the new number, then we will get a number which is less than 1100. We see that if we place 3 after 34 and multiply 3 with 343, we get 1029 which is less than 1100.
- Now 1100 - 1029 = 71 and we are placing 2 zeros after it so that it will be 7100. Now we have to add 3 with the divisor 343 which will be 346. Then we have to select a number to be placed beside this 346 in such a way that if we multiply this combined number with the new number, then we will get a number which is less than 7100. We see that if we place 2 after 346 and multiply 2 with 3462, we get 6924 which is less than 7100.
- So, we will get the quotient as 1.732 (corrected to three places of decimal).
4√3
= 4 × 1.732
= 6.928
<h3><u>Answer:</u></h3><u>6</u><u>.</u><u>9</u><u>2</u><u>8</u>
Hope it helps