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 ^(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)

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)

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

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

If I_(n)=int(x^(n))/(1+x^(2))dx, where n in N , then : I_(n+2)+I_(n)=

lim_(xto1)(x+x^(2)+x^(3)+…….+n^(n)-n)/(x-1) =……….,where n in N

Let a be a sequence such that al =3, an i 3a +1(n=1,2,3,..). If the value of and q are in their lowest form),then find the value of (p+q).. ?n (where p15

Let I_n=int_(-n)^n({x+1}*{x^2+2}+{x^2+3}{x^2+4})dx , where { } denote the fractional part of x. Find I_1.

Evaluate: inte^x(1+n x^(n-1)-x^(2n))/((1-x^n)sqrt(1-x^(2n)))dx

If I_(n)=int_(0)^(2)(2dx)/((1-x^(n))) , then the value of lim_(nrarroo)I_(n) is equal to