Let `P_n=prod_(k=2)^n(1-1/(^(k+1)C_2))`. If `lim_(n->oo)P_n` can be expressed as lowest rational in the form `a/b`, find the value of (a + b).

Let I_n=int_- 1^1|x|(1+x+(x^2)/2+(x^3)/3+.....+(x^(2n))/(2n))dx where n in N . If lim_(n->oo) I_n can be expressed as a ration number p/q in the lowest form, then find the value of p + q

Let l _(n) =int _(-1) ^(1) |x|(1+ x+ (x ^(2))/(2 ) +(x ^(2))/(3) + ..... + (x ^(2n))/(2n))dx if lim _(x to oo) l _(n) can be expressed as rational p/q in this lowest form, then find the value of (pq(p+q))/(10)

Let l _(n) =int _(-1) ^(1) |x|(1+ x+ (x ^(2))/(2 ) +(x ^(3))/(3) + ..... + (x ^(2n))/(2n))dx if lim _(x to oo) l _(n) can be expressed as rational p/q in this lowest form, then find the value of (pq(p+q))/(10)

If lim_(n rarr oo)sum_(k=1)^(n)(k^(2)+k)/(n^(3)+k) can be expressed as rational (p)/(q) in the lowest form then the value of (p+q), is

I_(n)=int_(-1)^(1)|x|(1+x+(x^(2))/(2)+(x^(3))/(3)+....+(x^(2n))/(2n))dx where n in N. If lim_(n rarr oo)I_(n) can be expressed as a ration number (p)/(q) in the lowest form,then find the value of p+q

Let S_(k), be defined as sum_(n=1)^(oo)((1)/(k))^(n) where k is positive integer greater than one.If the maximum value of expression (s_(k)*s_(k+2))/((s_(k+1))^(2))can be expressed in the lowest rational as (p)/(q). find the value of (p+q)

Let P=prod_(n=1)^(oo)(10^((1)/(2n-1))) then find log_(0.01)P

If the value of the sum n^(2) + n - sum_(k = 1)^(n) (2k^(3)+ 8k^(2) + 6k - 1)/(k^(2) + 4k + 3) as n tends to infinity can be expressed in the form (p)/(q) find the least value of (p + q) where p, q in N

If the value of the sum n^(2) + n - sum_(k = 1)^(n) (2k^(3)+ 8k^(2) + 6k - 1)/(k^(2) + 4k + 3) as n tends to infinity can be expressed in the form (p)/(q) find the least value of (p + q) where p, q in N