Home
Class 12
MATHS
Sum of the series a^n+a^(n-1)b+^(n-2)b^2...

Sum of the series `a^n+a^(n-1)b+^(n-2)b^2+………..+ab^n` can be obtained by taking outt `a^n or b^n` comon and using the forumula of sum of `(n+1)` terms of G.P. N the basis of above information answer the following question:Coefficientoif `xp, (0leplen) in 3^(n-1)+3^(n-2)(x+3)+3^(n-3)(x+3)^2+............+(x+30)^(n-1)` is (A) `^nC_p3^n-p)` (B) `^(n+1)C_p3^(n-p+1)` (C) `^nC_p3^(n-p-1)` (D) none of these

Promotional Banner

Similar Questions

Explore conceptually related problems

Sum of the series a^n+a^(n-1)b+^(n-2)b^2+………..+ab^n can be obtained by taking outt a^n or b^n comon and using the forumula of sum of (n+1) terms of G.P. N the basis of above information answer the following question: Coefficient of x^50 in (1+x)^1000+x(1+x)^999+........+x^999(1+x)+x^1000 is (A) ^1000C_50 (B) ^1002C_50 (C) ^1001C_50 (D) ^1001C_49

If the sum of n terms of a G.P.is 3-(3^(n+1))/(4^(2n)) then find the common ratio.

2.^(n)P_(3)=^(n+1)P_(3)

Sum of series : 1+2+3+......... +n is (A) ((n)(n+1))/2 (B) n(n+1) (C) ((n+1)(n+2))/2 (D) none of these.

If n is a positive integer such that (1+x)^n=^nC_0+^nC_1+^nC_2x^2+…….+^nC_nx^n, for epsilonR . Also ^nC_r=C_r On the basis o the above information answer the following questions for any aepsilon R the value of the expression a-(a-1)C_1+(a-2)C-2-(a-3)C_3+.+(1)^n(a-n)C_n= (A) 0 (B) a^n.(-1)^n.^(2n)C_n (C) [2a-n(n+1)[.^(2n)C_n (D) none of these

If the sum of n terms of an A.P.is 2n^(2)+5n then its nth term is 4n-3 b.3n-4 c.4n3 d.3n+4

Find n if .^(n-)P_(3): .^(n)P_(4) = 1:9 .

If the sum of n terms of an A.P is (4n^(2)-3n)/(4) then ,n^(th) term of the A.P