Home
Class 12
MATHS
Let a=3^(1/(223))+1 and for all geq3,l e...

Let `a=3^(1/(223))+1` and for all `geq3,l e tf(n)=^n C_0dota^(n-1)-^n C_1dota^(n-2)+^n C_2dota^(n-3)-+(-1)^(n-1)dot^n C_(n-1) a^0 . If the value of `f(2007)+f(2008)=3^k w h e r ek in N ,` then the value of `k` is.

Text Solution

Verified by Experts

The correct Answer is:
9
Promotional Banner

Topper's Solved these Questions

  • BIONMIAL THEOREM

    VK JAISWAL ENGLISH|Exercise Exercise-3 : Matching Type Problems|2 Videos

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

  • CIRCLE

    VK JAISWAL ENGLISH|Exercise Exercise - 5 : Subjective Type Problems|12 Videos

Similar Questions

Explore conceptually related problems

Let a=3^(1//224)+1 and for all n ge 3 , let f(n)=""^(n)C_(0)a^(n-1)-""^(n)C_(1)a^(n-2)+""^(n)C_(2)a^(n-3)+...+(_1)^(n-1)*""^(n)C_(n-1)*a^(0). If the value of f(2016)+f(2017)= 3^(k) , the value of K is

Let a=(2^(1//401)-1) and for each ngeq2,l e tb_n=^n C_1+^n C_2dota+^n C_3a^2+......+^n C_n*a^(n-1) . Find the value of (b_(2006)-b_(2005))dot

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

If .^(n+1)C_(r+1):^(n)C_(r):^(n-1)C_(r-1)=11:6:3 , find the values of n and r.

Find the sum 3^n C_0-8^n C_1+13^n C_2xx^n C_3+dot

If .^(n)C_(r-1): .^(n)C_(r): .^(n)C_(r+1)=3:4:5 , find the values of n and r.

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

Prove that: ^(2n)C_0-3.^(2n)C_1+3^2.^(2n)C_2-..+(-1)^(2n) ..3^(2n)^(2n)C_(2n)=4^n for all value of N

(n+2)C_0(2^(n+1))-(n+1)C_1(2^(n))+(n)C_2(2^(n-1))-.... is equal to

Find .^(n)C_(1)-(1)/(2).^(n)C_(2)+(1)/(3).^(n)C_(3)- . . . +(-1)^(n-1)(1)/(n).^(n)C_(n)