If `(1+x)^(2010)=C_(0)+C_(1)x+C_(2)x^(2)+ …….+C_(2010) x^(2010)` then the sum of series `C_(2)+C_(5)+C_(8)+ ……… +C_(2009)` equals to :

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+ . . .+C_(n)x^(n) , then the value of : C_(1)+2C_(2)+3C_(3)+ . . .+nC_(n) is:

If (1+x)^(15)=C_(0)+C_(1)x+C_(2)x^(2)+....+C_(15^(x^(15))) , then find the sum of 2 C_(2)+2.3 C_(3)+3.4 C_(4)+….+14.15 C_(15)

If (1 + x)^(n) = C_(0) + C_(1) x C_(2) x^(2) +…+ C_(n) x^(n) , then the sum C_(0) + (C_(0)+C_(1))+…+(C_(0) +C_(1) +…+C_(n -1)) is equal to

If (1 + x)^(n) = C_(0) + C_(1) x +C_(2) x^(2) +…+ C_(n) x^(n) , then the sum C_(0) + (C_(0)+C_(1))+…+(C_(0) +C_(1) +…+C_(n -1)) is equal to

If (1 + x)^(n) = C_(0) + C_(1) x C_(2) x^(2) +…+ C_(n) x^(n) , then the sum C_(0) + (C_(0)+C_(1))+…+(C_(0) +C_(1) +…+C_(n -1)) is equal to

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n) , then find the value of C_(0)+C_(2)+C_(4)+C_(6)+........ ​ ​

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + …+ C_(n) x^(n) , then for n odd, C_(1)^(2) + C_(3)^(2) + C_(5)^(2) +....+ C_(n)^(2) is equal to

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + …+ C_(n) x^(n) , then for n odd, C_(1)^(2) + C_(3)^(2) + C_(5)^(2) +....+ C_(n)^(2) is equal to

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) , find the sum of the series (C_(0))/(2) -(C_(1))/(6) + (C_(2))/(10) + (C_(3))/(14) -...+ (-1)^(n) (C_(n))/(4n+2) .

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then sumsum_(0lerltslen)(r+s)C_(r)C_(s) is equal to :