Home
Class 12
MATHS
Find the sum sum(j=0)^(n) (""^(4n+1)C(j)...

Find the sum `sum_(j=0)^(n) (""^(4n+1)C_(j)+""^(4n+1)C_(2n-j))`.

Text Solution

Verified by Experts

The correct Answer is:
`2^(4n)+.^(4n+1)C_(n)`
`underset(j=0)overset(n)sum(.^(4n+1)C_(j) + .^(4n+1)C_(2n-j))= (.^(4n+1)C_(0) + .^(4n+1)C_(1)+"....." .^(4n+1)C_(n))+(.^(4n+1)C_(2n)+.^(4n+1)C_(2n-1)+"....."+.^(4n+1)C_(n))`
`= (.^(4n+1)C_(0)+.^(4n+1)C_(1)+"...."+.^(4n+1)C_(2n))+.^(4n+1)C_(n)`
` = 2^(4n) + .^(4n+1)C_(n)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.5|8 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.6|10 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.3|7 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

Find the sum sum_(r=0)^n^(n+r)C_r .

Find the sum sum_(i=0)^r.^(n_1)C_(r-i) .^(n_2)C_i .

Find the sum sumsum_(i!=j)^ nC_i^n C_j

Find the sum sum_(r=1)^n r^2(^n C_r)/(^n C_(r-1)) .

Find the sum of sum_(r=1)^n(r^n C_r)/(n C_(r-1) .

Find the sum sum_(j=1)^(10)sum_(i=1)^(10)ixx2^(j)

Prove that sum_(r=0)^(2n)r(.^(2n)C_r)^2=n^(4n)C_(2n) .

Find the sum sumsum_(0lt=ilt=jlt=n)^ nC_i^n C_j

Prove that sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)

The sum sumsum_(0leilejle10) (""^(10)C_(j))(""^(j)C_(r-1)) is equal to