1ketan pls explain it...
6 Answers
1Its an A.G.P. series
S=1+2ω+3ω2+......+3nω3n-1 ......(1)
Sω=ω+2ω2+........+(3n-1)ω3n+3nω3n ......(2)
(1)-(2) is
S(1-ω)=1+ω+ω2+.......+ω3n-1 -3nω3n
after that wat ???
pls explain.......
262since 1,w,w2 are roots of x3=1 ,
sum of roots =0
or, 1+w+w2=0
similarly, w3+w4+w5=0 ..... and so on
thus S(1-w)= 0 +0+....0 - 3n (as w3=1)
or S= 3nw-1
1another way to do it,
consider the function f(x) = x + x2+x3....+x3n
we are required to find f'(w) .