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IGSTUDENT:

--- Quote from: astarmathsandphysics on November 10, 2009, 09:58:30 pm ---Thanks  a lot for the help. I still do not really understand Q2.
For Q1. It was actually show that an=3^(n-1) for all positive integers. sorry for they typo.


I also had another question.
how do you solve   5logx  +2 is greater than 0. where x is the base
and 3+lnx is greater than e^x?


Thanks.


. let a1,a2,a3,...be a sequence defined by
    a1=1,an=3an-1; n?1

    Show that an=3^n-1 for all positive integers n.


 Prove the following statement.
    n
2. ? 1/(2i-1)(2i+1)=n/2n+1       for each positive integer n.
    1

3. Use mathematical induction to prove that (5^n)+(9^n)+2 is divisible by 4,for n?Z+.

Thanks.
1.

SO p(1) is true. Suppose p(k) is true, prove p(k+1) trues
Are you sure this question is right?

2.

3.p(1) 5+9+2=16 hence p(1) is true
suppoose p(k) is true then (5^k)+(9^k)+2 is divisible by 4
p(k+1)-p(k) (5^(k+1))+(9^(k+1))+2-(5^k)-(9^n)-2  =5^k(5-1) +9^k(9-1)=4*5^k +8*9^k which is divisible by 4

--- End quote ---

astarmathsandphysics:
Will look when i get home

IGSTUDENT:
i needed some help with 2 questions

1. The quadratic equation ax^2+bx+c=0 has roots x=alpha and x=beta
    a) Express the product of roots, alpha*beta in terms of a and c

2. Find a quadratic function in the form y=x^2+bx+c the satisfies the given functions:
    The function has zeros of x=1/2 and x=3 and its graph passes through the point (-1,4)

Thanks

nid404:
I didn't quite get the first question...but i got the second one...so here it is

y=0 when x=1/2 or x=3


3eqns 3 variables...solve simultaneously
x=3
9y+3b+c=0
x=1/2
0.25y+0.5b+c=0
x=-1
1y-1b+c=4
y=2/3 b=-7/3 c=1
y=2/3x2-7/3x+1

IGSTUDENT:

--- Quote from: \m/ |\|!d \m/ on March 20, 2010, 03:05:54 pm ---I didn't quite get the first question...but i got the second one...so here it is

y=0 when x=1/2 or x=3


3eqns 3 variables...solve simultaneously
x=3
9y+3b+c=0
x=1/2
0.25y+0.5b+c=0
x=-1
1y-1b+c=4
y=2/3 b=-7/3 c=1
y=2/3x2-7/3x+1

Thanks, i made a mistake in the 1st Q. it is alpha *beta and not delta will that help?


--- End quote ---

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