" Determine "lim_(n rarr oo)sum_(k=1)^(n)(sin((pi/2)/(k))-cos((pi/2)/(k))-sin((pi/2)/(k+2))+cos((pi/2)/(k+2)))

lim_(n->oo)sum_(k=1)^n((sin)pi/(2k)-(cos)pi/(2k)-(sin)(pi/(2(k+2))+(cos)pi/(2(k+2)))=

Find the value of lim_(n rarr oo)sum_(k=1)^(n)((k)/(n^(2)+k))

lim_ (n rarr oo) sum_ (k = 1) ^ (n) ((sin) (pi) / (2k) - (cos) (pi) / (2k) - (sin) ((pi) / (2) k + 2)) + (cos) (pi) / (2 (k + 2))) =

Evaluate lim_(n rarr oo)sum_(k=1)^(n)quad (k)/(n^(2)+k^(2))

lim_ (n rarr oo) sum_ (k = 1) ^ (n) (k ^ (2)) / (2 ^ (k))

sum_(m=1)^(32)m[sum_(k=1)^(6)sin2k(pi)/(7)-i cos2k(pi)/(7)]

lim_(n rarr oo)n sin\ (2 pi)/(3n)*cos\ (2 pi)/(3n)

The value of Lim_(n rarr oo)sum_(k=1)^(n)(n-k)/(n^(2))cos((4k)/n) equals