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Mathematics 16 Online
OpenStudy (aravindg):

last minute help

OpenStudy (anonymous):

what's up?

OpenStudy (aravindg):

find sum upto n terms 8,88,888,8888.................

OpenStudy (nottim):

Help help help.

OpenStudy (nottim):

I like to help.

OpenStudy (nottim):

Me too.

OpenStudy (anonymous):

Is it very hard ?

OpenStudy (aravindg):

more qns in que

OpenStudy (aravindg):

lol

OpenStudy (aravindg):

after this next qn

OpenStudy (anonymous):

what have you tried in this problem ?

OpenStudy (aravindg):

taking 8 common

OpenStudy (anonymous):

and ?

OpenStudy (anonymous):

its all about GP a= 8 r= 88/8=11 sum(n)= 8(11^n -1) ---------- 10

OpenStudy (aravindg):

hey dashini i dont think r is 11

OpenStudy (anonymous):

This not a geometric progression

OpenStudy (aravindg):

ya

OpenStudy (anonymous):

this question does involve a geometric series though (its hiding)

OpenStudy (aravindg):

how?

OpenStudy (anonymous):

The nth term is given by \( T_n=\large \frac{8\times(10^n-1)}{9} \)

OpenStudy (anonymous):

its a linear recursive function a(r+1) = 10*a(r) + 8

OpenStudy (aravindg):

i need sm upto n

OpenStudy (anonymous):

Dhashni??? come to my post!

OpenStudy (aravindg):

sum

OpenStudy (anonymous):

something for which you should try using your head first ? :P

OpenStudy (anonymous):

\[8+88+888+8888+\cdots+888\ldots 88\]\[=8(1+11+111+1111+\ldots+111\ldots 11)\] 1111...111 is the same as:\[1+10+100+\ldots+ 10^{n-1}=\frac{10^n-1}{9}\]

OpenStudy (aravindg):

hey joe u shud write n instead of 1

OpenStudy (aravindg):

isnt it???

OpenStudy (anonymous):

nopes joe wrote right.

OpenStudy (anonymous):

so like others have said, you are looking for:\[\sum_{n=0}^n8\cdot \frac{10^n-1}{9}\]

OpenStudy (anonymous):

8/9(10n\[8/9\ 10n+100-10^{n}\10]\]

OpenStudy (aravindg):

so wat is final answr?

OpenStudy (anonymous):

\( \sum_{k=0}^n8\cdot \frac{10^k-1}{9} = \frac{8}{81} 10(10^n-1)-9n \)

OpenStudy (anonymous):

that should be pretty straight forward to calculate. pull out the 8/9, and split of other part with addition.

OpenStudy (anonymous):

*substraction i mean.

OpenStudy (anonymous):

btw joe, \( \sum_{n=0}^n \) is ambiguous :P

OpenStudy (anonymous):

yeah, i just noticed lolol >.<

OpenStudy (aravindg):

ya wt shud i giv as final amnswr??

OpenStudy (anonymous):

hehe :D

OpenStudy (anonymous):

should have made my dummy variables i instead.

OpenStudy (anonymous):

give whatever you get when you calculate the sum.

OpenStudy (aravindg):

next qn :what is slope of x/a +y/b=1

OpenStudy (anonymous):

b/a

OpenStudy (aravindg):

hw u got that???

OpenStudy (anonymous):

missing the negative.

OpenStudy (akshay_budhkar):

-b/a

OpenStudy (anonymous):

ya.. it's -b/a

OpenStudy (anonymous):

\[4(n(n+1)) - 8/9 *n +8/81 * (1-10^n)\]

OpenStudy (anonymous):

convert the equation into slope form..

OpenStudy (akshay_budhkar):

two ways of getting that slope write it in the form y=mx+C

OpenStudy (akshay_budhkar):

or the slope of a line ax+by=c is -a/b remember that

OpenStudy (anonymous):

you in which grade?

OpenStudy (aravindg):

next qn:::cos20cos40cos80=1/8 prove this!!

OpenStudy (akshay_budhkar):

me? :P

OpenStudy (anonymous):

Have you considered trying this elementary problems yourself first ?

OpenStudy (akshay_budhkar):

yea aravind try it yourself

OpenStudy (anonymous):

use the formula ....cosx * cosy = [cos(x+y) +cos(x-y)]/2

OpenStudy (anonymous):

\[\cos \theta * \cos(60-\theta)*\cos(60+\theta)=\cos3\theta\]

OpenStudy (aravindg):

then how 1/8???

OpenStudy (anonymous):

as they say we given you all the data required to find the solution give it a try.

OpenStudy (aravindg):

i am getting 1/2 :(((

OpenStudy (akshay_budhkar):

you saw him now ffm? he is here from past half hour

OpenStudy (anonymous):

it's 1/4cos60..

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