sigma qs (1 Viewer)

MrBrightside · Dec 7, 2010

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I get that it is an AP and GP.

just how does it = 443? i [get 441 for the AP and 1.99999 for the GP].

FTW · Dec 7, 2010

You need to split it up into two seperate sums I believe, and then add them together? So what you said is pretty much 441+2 = 443?
This is without me actually attempting the question, I'm going on the information you have.

hscmathstutor10 · Dec 7, 2010

for AP ie (1+2n)

we have first term = 1 , and difference =+2, number of terms = n=20

S n = (n/2) ( 2a + (n-1) d ) = 20/2 ( 2 (1) + 19(2) ) = 10 ( 40) = 400

for the GP ie ( (1/2)^n )

a= 1, r= (1/2) , n=20

S (n) = a (1-r^(n) ) / (1-r) = 1 ( 1- (1/2)^20 ) / ( 1-1/2 ) = 2 ( 1- (1/2)^20 )

then add the two together

MrBrightside · Dec 7, 2010

so the 1.999 gets round up ? is the gp 441?

hscmathstutor10 · Dec 7, 2010

lol I made a mistake, there are 21 terms, as we start at n=0 ( not n=1 as we usually do )

so the final answer should be = (21/2) ( 2(1) +20(2) ) + 2 ( 1-(1/2)^21 )

MrBrightside · Dec 7, 2010

hscmathstutor10 said:
lol I made a mistake, there are 21 terms, as we start at n=0 ( not n=1 as we usually do )

so the final answer should be = (21/2) ( 2(1) +20(2) ) + 2 ( 1-(1/2)^21 )

your wrong bro ... it doesn't equal 461.99

ohexploitable · Dec 7, 2010

MrBrightside said:
your wrong bro ... it doesn't equal 461.99

You entered the expression into your calculator wrong

Oh.

The irony.

ibbi00 · Dec 7, 2010

I think it's time you got yourself a tutor considering the multitude of threads you've started in the past 48 hours.

MrBrightside · Dec 7, 2010

ohexploitable said:
You entered the expression into your calculator wrong

Oh.

The irony.

442.99999999999999999999 sry my mistake. so i'm guessing it rounds up? ^^

hscmathstutor10 · Dec 7, 2010

MrBrightside said:
442.99999999999999999999 sry my mistake. so i'm guessing it rounds up? ^^

yes, the sum [n=0..20] (1/2)^n converges to 2 , its ratio is less than one and therefore has a limiting sum a/ ( 1-r) = 1/ ( 1-1/2) =2

as n gets larger and larger the sum approches 2

Alkanes · Dec 7, 2010

ibbi00 said:
I think it's time you got yourself a tutor considering the multitude of threads you've started in the past 48 hours.

Agreed

sigma qs (1 Viewer)

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