Let S be the sum of the first 9 terms of the series :
`{x+ka}+{x^(2)+(k+2)a}+{x^(3)+(k+4)a}+{x^(4)+(k+6)a}+...` where `a!=0` and `a!=1`.
If `S=(x^(10)-x+45a(x-1))/(x-1)`, then k is equal to :

If x^(6)+1/(x^(6))=k(x^(2)+1/(x^(2))) then k is equal to

If (x-4)/(x^(2)-5x-2k)=2/(x-2)-1/(x+k), " then "k=

If sum of series (x+ka)+(x^2+(k-2)a)+(x^3+(k-4)a)+...9 terms is ((x^10-x-45a(x-1))/(x-1)) then value of k is:

Let S_k be the sum of first k terms of an A.P. What must this progression be for the ratio (S_(k x))/(S_x) to be independent of x ?

If sum of the first 21 terms of series log _((1)/( 9 ^(2))) x + log _((1)/(9 ^(3))) x + log _((1)/( 9 ^(4))) x + ..., where x gt 0 is 504, then x is equal to :

If (x-4)/(x^(2)-5x-2k)=(2)/(x-2) - (1)/(x+k) , then find k ?

If (x-4)/(x^(2)-5x+2k)=(2)/(x-2) - (1)/(x-k) , then find k ?

Suppose k in R . Let a be the coefficient of the middle term in the expansion of (k/x+x/k)^(10) and b be the term independent of x in the expansion of ((k^(2))/x+x/k)^(10) . If a/b=1 , then k is equal to

If (3x-6)/((x-6)(x+k))=2/(x-6)+1/(x+k) " then " k=