" 4."quad 3C_(0)-8C_(1)+13C_(2)-18C_(3)+..." upto "(n+1)" terms "=0

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+C_(n)x^(n) prove that 3C_(0)-8C_(1)+13C_(2)-18C_(3)+...up rarr(n+1)terms=0

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : 3.^(n)C_(0)-8.^(n)C_(1)+13.^(n)C_(2)-18.^(n)C_(3)+....."up to"(n+1)"terms" =0

Show that 3C_0-8C_1 + 13C_2 - 18C_3 + ..... + (n+1)^(th) term = 0

If (1+x)^n=C_0+C_1x+C_2x^2+……..+C_nx^n in N prove that (a) 3 C_0- 8C_1+13C_2-18C_3+...."upto" (n+1) term=0 if n ge 2 (b ) 2C_0+2^2(C_1)/(2)+2^3(C_2)/(3)+2^4C_(3)/4+....+2^(n+1)(C_n)/(n+1)=(3^n+1-1)/(n+1) ( c) C_0^2+(C_1^2)/2+C_2^2/3+....+C_n^2/(n+1)=((2n+1)!)/(((n+1)!)^2)

If n is positive integer greater than 1, then 3 (""^(n) C_(0)) -8(""^(n) C_(1)) + 13 (""^(n)C_(2)) +… upto (n+1) terms =

lf C_(r)=""^(n)C_(r) , then C_(0)-1/3C_(1)+1/5C_(2) …… upto (n+1) terms equal

Find the sum 3^n C_0-8^n C_1+13^n C_2-18^n C_3+dot +.....+(n+1)terms

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0