IIT JEE , AIEEE Forum - Mathematics , Algebra

neeraj_agarwal_1990

Question:

Value of (ln i) + (ln i) ² + (ln i) ³ +..... + (ln i) ⁿ is:

Options:

A.

B.	n(n + 1) ln i

C.

D.	None of these

Answer

Answer:

C

Conjurer

Stupid mistake.Please boink me

dinesh_ddt

i = e^ipi/2
now ln i is i*pi/2...!!!!!!!!!!

dinesh_ddt

then ull get a G.P wich can be solved easily

elastiboysai

@conjurer lni=ipi/2 not e^/2

Greatdreams

ln i + ( ln i ) ² + ( ln i ) ³ + ......(ln i ) ⁿ

So its a G.P

Sum

1st term = ln i = i.

/2

So sum = i.

/2 [ 1 - ( i.

/2 ) ⁿ ] / [ 1 - i

/2 ]

= i.

/2 [ 1 - (i.

/2) ⁿ ] * ( 1 + i.

/2 ) / (1 +

²/4 )

={ i.

/2 [ 2 ⁿ - (i

)ⁿ] * (2 + i

) /2 } / (4 +

² )

= {[ 2ⁿ - (i

) ⁿ] ( 2

i -

² )} / 2 ⁿ (

² + 4)

For objective problems this should be good.

Here you can easily see the answer is coming like that

This has been discussed before.

kishore.subramanian.b

ln i =

/2 e^i/2

given series is

/2 e^i/2, (

/2 e^i/2)^{2 ,},(

/2 e^{i/2) 3},...........^,,(

/2 e^{i/2) n}

sum is

/2 e^i/2( (

/2 e^i/2)ⁿ-- 1) / ( (

/2 e^i/2)-- 1)

= i

/2 ( (

/2 i)ⁿ-- 1) / ( (

/2 i)-- 1)

= i

/2 ( (

i)ⁿ-- 2ⁿ) / 2ⁿ( (

i)-- 2) *2

= i

( 2ⁿ--(

i)ⁿ ) ((

i)+ 2 ) / 2ⁿ( 4 +

²)

=

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