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secondary 3 | A Maths
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need help with the circled questions, pls explain too :)
Date Posted: 3 years ago
Views: 508
Say more words like, thks very much, deeply appriciate when someone spend time help you, dun just keep asking questions without thks
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This method of cancellations is known as the method of differences. The sum is made simple because the majority of the terms present in the full series actually cancel out, leaving behind a tiny minority of surviving terms to be calculated easily.
Date Posted:
3 years ago
i dont really understand the first 4 columns of the expansion in part b. also, why is it minus but not plus or times tho
The fraction we have decomposed into is 1 / (x + 1)(x + 2) = 1 / (x + 1) - 1 / (x + 2).
When x = 1, we have
1 / (2) (3) = 1/2 - 1/3
When x = 2, we have
1 / (3) (4) = 1/3 - 1/4
The rest is similar.
The sum of all these goes like this.
1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ... + ... + 1/197 - 1/198 + 1/198 - 1/19 9 + 1/199 - 1/200
and you will see that there are many pairs cancelling out (1/3 against 1/3, 1/4 against 1/4 and so on, up to 1/199 against 1/199).
Surviving are the 1/2 and the -1/200, so combining these two, we get sum = 1/2 - 1/200 = 99/200.
When x = 1, we have
1 / (2) (3) = 1/2 - 1/3
When x = 2, we have
1 / (3) (4) = 1/3 - 1/4
The rest is similar.
The sum of all these goes like this.
1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ... + ... + 1/197 - 1/198 + 1/198 - 1/19 9 + 1/199 - 1/200
and you will see that there are many pairs cancelling out (1/3 against 1/3, 1/4 against 1/4 and so on, up to 1/199 against 1/199).
Surviving are the 1/2 and the -1/200, so combining these two, we get sum = 1/2 - 1/200 = 99/200.
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An idea
Date Posted:
3 years ago
why is logx4 the same as 1/log4x tho
logx 4
= log4 4 / log4 x (we change the logarithm to a new base 4 using the change of base rule)
= 1 / log4 x (since log4 4 = 1)
= log4 4 / log4 x (we change the logarithm to a new base 4 using the change of base rule)
= 1 / log4 x (since log4 4 = 1)
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This shall be the last one I do for today. The rest I do another time if I can remember and I have free time.
Date Posted:
3 years ago
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Q10i, Q10ii, Q10iii
Date Posted:
3 years ago
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Q10iv, Q10v
Date Posted:
3 years ago
sorry!! i did not mark this qn as done previously, but tyvm for helping me through this qn :)
anyways, are you able to help these few days? need help with some topics
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