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The sum 3 .^(n)C(0)-8.^(n)C(1)+13 .^(n)C...

The sum `3 .^(n)C_(0)-8.^(n)C_(1)+13 .^(n)C_(2)-18xx.^(n)C_(3)+....` is less than

A

1

B

3

C

4

D

5

Text Solution

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The correct Answer is:
A, B, C, D
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Explore conceptually related problems

Find the sum 3^(n)C_(0)-8^(n)C_(1)+13^(n)C_(2)xx^(n)C_(3)+...

If .^(n)C_(8)=.^(n)C_(6) , find .^(n)C_(3) .

Knowledge Check

  • The value of the sum of the series 3.""^(n)C_(0)-8" "^(n)C_(1)+13" "^(n)C_(2)-18" "^(n)C_(3)+ …….. upto (n+1) terms is

    A
    0
    B
    `3^(n)`
    C
    `5^(n)`
    D
    none of these

  • The value of .^(n)C_(0) xx .^(2n)C_(r) - .^(n)C_(1)xx.^(2n-2)C_(r)+.^(n)C_(2)xx.^(2n-4)C_(r)+"…." is equal to

    A
    `.^(n)C_(r-n) xx 2^(2n-r)` if `r ge n`
    B
    0, if `r lt n`
    C
    `.^(n)C_(r-n) xx 2^(n-r)` if `r ge n`
    D
    `.^(-n)C_(r-n) xx 2^(2n-r)` if `r lt n`

    • Similar Questions

    Explore conceptually related problems

    Find the following sums : (i) .^(n)C_(0)-.^(n)C_(2)+.^(n)C_(4)-.^(n)C_(6)+"....." (ii) .^(n)C_(1)-.^(n)C_(3)+.^(n)C_(5)-.^(n)C_(7)+"...." (iii) .^(n)C_(0)+.^(n)C_(4)+.^(n)C_(8)+.^(n)C_(12)+"....." (iv) .^(n)C_(2) + .^(n)C_(6) + .^(n)C_(10)+.^(n)C_(14)+"......" (v) .^(n)C_(1) + .^(n)C_(5)+.^(n)C_(9)+.^(n)C_(13)+"...." (vi) .^(n)C_(3) + .^(n)C_(7) + .^(n)C_(11) + .^(n)C_(15) + "....."

    Find the sum .^(n)C_(0) + 2 xx .^(n)C_(1) + xx .^(n)C_(2) + "….." + (n+1) xx .^(n)C_(n) .

    Prove that .^(n)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3) + "……" + (-1)^(r) + .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ) .

    Let n in N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms ""^(n) C_(0) , 3 .""^(n)C_(1) , 5. :""^(n) C_(2) , & .""^(n)C_(3) is equal to 2 ^(100) . 101 then 2 [(n-1)/(2)] is equal to _________

    Prove that (r+1)xx.^(n)C_(0)-rxx.^(n)C_(1)+(r-1)xx.^(n)C_(2)-(r-2).^(n)C_(3) + "...."+(-1)^(r)xx.^(n)C_(r)+"...."=(-1)^(r)xx.^(n-2)C_(r) .

    Find the sum .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "……" + n xx .^(n)C_(n) .

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