`n/2 - (3n)/4 +(5n)/6 = 21`

The value of lim_(n to oo) (2n^(2) - 3n + 1)/(5n^(2) + 4n + 2) equals

In the binomial expansion of (a-b)^(n),n>=5 the sum of 5 th and 6 th terms is zero,then (a)/(b) equals (1)(5)/(n-4) (2) (6)/(n-5) (3) (n-5)/(6) (4) (n-4)/(5)

Solve : (2)/(3)(n+6) - (1)/(5)(n-4) = (3)/(7)(n+12)

The ratio of the sums of n terms of two Aps is (3n-13) : (5n+21) . Find the ratio of the 24th terms of the two progressions.

lim_ (n rarr oo) ((1 + 2 ^ (4) + 3 ^ (4) + ...... + n ^ (4)) / (n ^ (5))) - lim_ (n rarr oo ) ((1 + 2 ^ (6) + 3 ^ (6) + .... + n ^ (6)) / (n ^ (7)))

If the sum of n term of the series (5)/(1.2.3) + (6)/(2.3.4) + ( 7)/(3.4.5)+"…." is a/2 - (n+b)/((n+1)(n+2)) , then

Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))