IIT JEE , AIEEE Forum - Mathematics , Algebra

rich_1986

-1-

-1-..............

infinitestrength

if infinity is even then soln is 0
if infinity is odd then soln is "i"

spideyunlimited

infinty is neither even nor odd...
rich_1986 i think ur question is wrong...
the one we CAN solve is where there are all + signs not - sign

and the under root sign is over all of them naa?

spideyunlimited

anyway i think the answer is i/2 (iota / 2)

let .. root -1 - root -1 - root -1... upto infinity = y

then y = root -1 - y
2y = root - 1
y = i /2

*PLZ RATE*

rajatsen91

let x= root -1 - root -1 - root -1...
x^2=-1-x
therefore x^2+x+1=0
so
(x+w)(x+w^2)=0
therefore x= w or w^2 ( where w and w^2 are the complex cube roots of unity)

rajatsen91

The question is right and infinite strength you have the word infinite in your profile name and you do not even know that infinity is not a real number.

b_srikalyan009

the question is not what u think.only rajetsen is right

it goes in this way

hence if y is the ans

y=^{[2 ]}

(-1-y)

squaring on both the sides

y^2= -1-y

y^2+y+1=0

hence ans is w & w^2

mikans

the ans is 1/2 i suppose

metal

We know that

-1 = i

so, the question can be written as i-i-i-i.........till infinity, [if I have understood the question properly.]

The first two i cancel out. So the expression becomes -i-i-i-....till infinity.

Take the negative sign common.

you get -{i+i+i........till infinity}

the thing within the bracket is an infinite A.P. with common difference > 0 and the sum of such a series is always = infinity.

So the final answer is {-infinity}, if my interpretetion of your question is correct.

please rate me

b_srikalyan009

@metal i dont think the is in that way.
in that case u cannot solve the question.
what i and rajetsen did is absolutely right.
otherwise the question makes no sense.
what i have done is i assumed the summation to be y.
if u ignore one term in is the same as the sum is to infinity.

metal

Yes, I get it. I was wrong. Thank you.

spideyunlimited

read my method above n temme whts wrong with it then

mk_suhas

hey spideyunlimited, this is where u have gone wrong

when

-1-

-1-..............

u took y =

-1-

-1-.............. ok i agree
later, y =

-1-y

now the mistake is, u have taken 2y = i
actually, the y is within brackets, so it can't be taken as 2y

So here's the solution..
y² = + or - (-1-y)

now go on n get 2 solutions!

Ask & Discuss Questions with Community & Experts