1
Anvay Vaidya
·Nov 21 '08 at 3:59
i totally agree whd nishant.........
1
°ღ•๓ÑÏ…Î
·Nov 21 '08 at 4:00
hmmm....
-(ln(1-x)=x+x^2/2+x^3/3.......
diff it we get
1/(1-x)=1+x+x^2+x^3..........
diff again we get
(-1)/(1-x)^2=1+2x+3x^2+4x^3.......
nw multiplyin by x we get
(-x)/(1-x)=x+2x^2+3x^3.......
just substitute x=x+1
u get ur question ........ie
(1-)(x+1)/(-x)=(1+x)+2(1+x)^2+3(1+x)^3............
so u basically need 2 find d ter x^50 in (1+1/x)........
wich u can find i guess
(m bad at that part :()
1
Rohan Ghosh
·Nov 21 '08 at 4:05
hey here your exp. goes up to infinity!!
but in the question it is upto 1000
you cant do that!!
1
champ
·Aug 22 '09 at 6:04
I am not getting the answer by Nishant's method :-(
1
Kalyan Pilla
·Aug 22 '09 at 11:18
There is no term of x50 until 50(1+x)50
So the coefficient of x50 is derived from........
50(1+x)50+51(1+x)51+52(1+x)52+....+1000(1+x)1000, whose value is...
=5050C50+5151C50+5252C50+.....+10001000C50
I am not very good at Binomial, so I dont know if Anything can be done beyond what I got[3]
Someone please try [5]
62
Lokesh Verma
·Aug 23 '09 at 23:57
y=1+x
the given sum is Σn.yn
(1−y)2y(1000y1001−1001y1000+1)
put back y=1+x
(x)2x+1(1000(x+1)1001−1001(x+1)1000+1)
this is same as finding the coeff of x50 in the above expression.
which is same as finding the coeff of x^52 in 1x+1(1000(x+1)1001−1001(x+1)1000+1)
I hope this helps now :)