Selangor Trial 2025 Add Maths Paper 1, Question 3
Solved on video in English · 5:11 video
The question
If a is the first term and r is the common ratio of a geometric progression, show that the sum to infinity of the progression is S∞ = a/(1 − r), where |r| < 1.
Given that the geometric progression is x, −(2/3)x, (4/9)x, −(8/27)x, …, find the sum to infinity of the progression in terms of x.
5:11Part (a)
Step 1
The sum of the first n terms of a geometric progression is Sₙ = a(1 − rⁿ)/(1 − r).
Why this step
The sum to infinity is what Sₙ settles on as n grows without end, so we build it from the formula for Sₙ.
3 more steps, each with the reason for it, in the full solution
Final answer
Shown
Where students lose marks
Don't jump to the formula: state that rⁿ → 0 because |r| < 1, or you lose the 'show that' marks.
Part (b)
5 more steps, each with the reason for it, in the full solution
Final answer
S∞ = (3/5)x
Where students lose marks
Watch out: 1 − (−2/3) = 1 + 2/3 = 5/3, not 1/3. Getting this wrong gives 3x instead of (3/5)x.
Watch every step of this question solved on video (5:11), with the reason behind each step and a box that checks your own answer.
No card. Every past-year question on video, in English and BM.
Questions are re-typeset by Eduly for study and commentary. Eduly is not affiliated with Lembaga Peperiksaan Malaysia or the Ministry of Education.