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primary 5 | Maths
| Fractions
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Date Posted: 5 years ago
Views: 553
= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +.... + 1/8 - 1/9 + 1/9 - 1/10
Notice a pattern?
-1/2 is cancelled out by + 1/2
-1/3 is cancelled out by + 1/3
-1/4 is cancelled out by + 1/4
And so on.
The only terms left are 1/1 and -1/10
So,
1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +.... + 1/8 - 1/9 + 1/9 - 1/10
= 1/1 - 1/10
= 10/10 - 1/10
= 9/10
Notice a pattern?
-1/2 is cancelled out by + 1/2
-1/3 is cancelled out by + 1/3
-1/4 is cancelled out by + 1/4
And so on.
The only terms left are 1/1 and -1/10
So,
1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +.... + 1/8 - 1/9 + 1/9 - 1/10
= 1/1 - 1/10
= 10/10 - 1/10
= 9/10
See 1 Answer
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The terms will cancel each other all the way until 1/9.
After all the cancellations, the surviving terms are 1/1 and -1/10, and of course 1/1 - 1/10 = 9/10.
This method is also known as the method of differences.
After all the cancellations, the surviving terms are 1/1 and -1/10, and of course 1/1 - 1/10 = 9/10.
This method is also known as the method of differences.
Date Posted:
5 years ago
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