O-Level Additional Math

[archie2]

Can someone explain this question on Geometric series

Sn = a*(1-r^n)/(1-r)

Question: For what values of the common ratio r will the sum to infinity of a geometric series exists?

Answer given: the sum of infinity of a geometric exists if and only if -1<r<1 and is equals to a/(1-r)

Doubt : why does the sum of infinity of a geometric does not exist if -1<r>1?
i thought the sum of infinity of the geometric series will be very large and exists in either -ve or +ve sum. OR could I have misinterprete the question?

[pinkapple]

AP, GP was previously introduced in AMath at O levels but taken out since 2008 or earlier.


nonethless, it can be in IP so still secondary.

[lost boy]

Urgent! Please answer as quickly as possible. I have no idea whether this is related to mathematics because its an arithmetic progressions question. This is a Secondary one question


Q1. Find the sum of the first N odd numbers.
Q2. Find the sum of the first n natural numbers
Q3. Write down three integers in A.P whose produce is a prime number

[pinkapple]

lost boy:

Urgent! Please answer as quickly as possible. I have no idea whether this is related to mathematics because its an arithmetic progressions question. This is a Secondary one question


Q1. Find the sum of the first N odd numbers.
Q2. Find the sum of the first n odd numbers
Q3. Write down three integers in A.P whose produce is a prime number

eh.. 1st 2 questions same mah

[lost boy]

I had changed q 2 . Ps show me the working . Thanks.

[pinkapple]

answer to Q2: http://www.9math.com/book/sum-first-n-natural-numbers

look at the picture. it'll help.

from here, try to answer Q1 yourself.

As for Q3, think what is the definition of prime numbers.
then what are integers.
work from here. tell u the answer tmrw.

[S-H]

Hi can someone help me with this question, thank you!


The curve y=ax^3+bx^2+c passes throught the points (-1,0) and (0,5). If the tangent to the curve at the point x=1 is parallel to the x-axis, find the values of a, b and c.

[jieheng]

S-H:

Hi can someone help me with this question, thank you!


The curve y=ax^3+bx^2+c passes throught the points (-1,0) and (0,5). If the tangent to the curve at the point x=1 is parallel to the x-axis, find the values of a, b and c.

y=ax^3+bx^2+c

x=0 , y=5
=> c = 5

x= -1 , y=0
0 = -a+b+c
=> a - b = 5 -----(1)

dy/dx = 3ax^2 + 2bx

At x=1 , dy/dx = 0

3a + 2b = 0 -----(2)

Solving equations (1) and (2) ,

a = 2

b = -3

[S-H]

Thank you jieheng!

[S-H]

Hi Jieheng, I have one more question to ask:-


A woman invested an amount of money in a firm and earned a simple interest of $54 each year. In a certain year when the company was not performing well, the interest rate was decreased by 0.25%, and the annual interest received dropped to $47.20. How much money did she invest?

Thanks in advance!