`C_1 +2.5C_2 +3.5^2 C_3+----- =`

The value of 1^2.C_1 + 3^2.C_3 + 5^2.C_5 + ... is

Consider the curves C_1 : x=0,C_2 :y =0, C_3 y =x^(2) +1, C_4 :y=2 ,C_5 : x =1 the area enclosed between the curves C_1 ,C_2 ,C_3 and c_5 is ( in square units ) -

The value of the determinant ∣5_C_0 5_C_1 5_C_2 5_C_3 5_C_4 5_C_5 1 4 1 1∣ is (A) 0

Show that: C_1 + C_2 + C_3 +..........+ C_5 = 31

""^4C_1 + ""^5C_2.(1/2) + ""^6C_3.(1/2)^2+….. to oo terms :

[(. ^nC_0+^n C_3+)-1/2(.^n C_1+^n C_2+^n C_4+^n C_5]^2 + 3/4(.^n C_1-^n C_2+^n C_4 +)^2= equals to a. 3 b. 4 c. 2 d. 1

^5C_1+^5C_2+^5C_3+^5C_4+^5C_5 is equal to