Given sum can be written as\nlim\nn!1\nXn\nk=1\n1\nn\n(\nk\nn\n) sec2 k2\nn2\nwR hich is limit of Riemann sum of f(x) = x sec2 x over the interval [0,1]. Thus the limit of required sum is 1\n0 [x sec2(x2)]dx = (tan 1)=2.

raju , 10 Years ago

Grade 12