AC Lim's answer to KKK's Secondary 1 Maths Singapore question.
done
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clear
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Need to crack our head 1st.... hope this helps
Date Posted:
3 years ago
For c), I think they are supposed to use the pattern above :
1/(1x2) + 1/(2 x 3) + 1/(3 x 4) + 1/(4 x 5) + ... + 1/(2019 x 2020) + 1/(2020 x 2021)
= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/2019 - 1/2020 + 1/2020 - 1/2021
Notice the common terms cancel out.
(-1/2 + 1/2 = 0, -1/3 + 1/3 = 0, -1/4 + 1/4 = 0, -1/2020 + 1/2020 = 0, etc)
We are left with 1 and -1/2021
So this becomes :
= 1 - 1/2021
= 2021/2021 - 1/2021
(Make common denominator)
= 2020/2021
1/(1x2) + 1/(2 x 3) + 1/(3 x 4) + 1/(4 x 5) + ... + 1/(2019 x 2020) + 1/(2020 x 2021)
= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/2019 - 1/2020 + 1/2020 - 1/2021
Notice the common terms cancel out.
(-1/2 + 1/2 = 0, -1/3 + 1/3 = 0, -1/4 + 1/4 = 0, -1/2020 + 1/2020 = 0, etc)
We are left with 1 and -1/2021
So this becomes :
= 1 - 1/2021
= 2021/2021 - 1/2021
(Make common denominator)
= 2020/2021
Edited
Yes. @J is right. It should be related to question a).
I didn’t check on question a) as @kkk need help on CnD ;)
I didn’t check on question a) as @kkk need help on CnD ;)
Nice deduction and working based on c) alone! This would be the real challenge without the help from the pattern (ala Olympiad style)
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