Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
secondary 4 | E Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
Need help with the circled one
Date Posted: 3 years ago
Views: 251
Use the property a² - b² = (a + b)(a - b)
(1 - 1/20²)
= (1² - (1/20)²)
= (1 + 1/20)(1 - 1/20)
= (21/20)(19/20)
Likewise,
(1 - 1/19²)
= (1² - (1/19)²)
= (1 + 1/19)(1 - 1/19)
= (20/19)(18/19)
(1 - 1/20²)
= (1² - (1/20)²)
= (1 + 1/20)(1 - 1/20)
= (21/20)(19/20)
Likewise,
(1 - 1/19²)
= (1² - (1/19)²)
= (1 + 1/19)(1 - 1/19)
= (20/19)(18/19)
Put this all together, we get :
(21/20)(19/20)(20/19)(18/19)(19/18)(17/18)(18/17)...(3/4)(4/3)(2/3)(3/2)(1/2)
Notice that most of the fractions can cancel out to give 1.
Eg. 19/20 x 20/19 = 1
This simplifies to :
(21/20)(1/2)
= 21/40
(21/20)(19/20)(20/19)(18/19)(19/18)(17/18)(18/17)...(3/4)(4/3)(2/3)(3/2)(1/2)
Notice that most of the fractions can cancel out to give 1.
Eg. 19/20 x 20/19 = 1
This simplifies to :
(21/20)(1/2)
= 21/40
See 1 Answer
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
There you go! Let us know if you have questions! Hope it is right!
Date Posted:
3 years ago
360 Tutoring Program