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BINOMIAL THEOREM | USE OF COMPLEX NUMBER...

BINOMIAL THEOREM | USE OF COMPLEX NUMBERS IN BINOMIAL THEOREM, SUM OF SERIES, MISCELLANEOUS SERIES | Find the sum `C_0-C_2+C_4-C_6+.........., where C_r = nC_r`, If `(1+x+x^2)^n=a_0+a_1x+a_2x^2+........a_(2n)x^(2n);` Find the value of `a_0+a_3+a_6+........;ninN`, Find the value of `4nC_0 + 4nC_4 + 4nC_8 + 4nC_12+...+4nC_(4n) `, Important facts and formula to find Sum of Series.Find the sum of `C_0+3C_1+3^2C_2+.......3^nC_n`., If `(1+x)^n=sum_(r=0)^n C_rx^r` then prove that `C_1+2C_2+3C_3+.....+nC_n=n2^(n-1)`, If `(1+x)^n=sum_(r=0)^n C_r x^r` , then prove that `C_0+C_1/2+.........+C_n/(n+1)=(2^(n+1)-1)/(n+1)`, `mC_r+mC_(r-1) nC_1+mC_(r-2)nC_2+...........+nC_r=(m+n)C_r` , where r < m, r < n, Find: `(nC_0)^2+(nC_1)^2+(nC_2)^2+.......+(nC_n)^2`, `(nC_0)^2-(nC_1)^2+(nC_2)^2+.....+(-1)^n(nC_n)^2`

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