Summation of series by integration let tx) be a continuous function defined on the closed intervai t =) dx lim n o rule: here we proceed as follows (i) (ii) exp

Summation of series by Integration Let TX) be a continuous function defined on the closed intervai t =) dx Lim n o Rule: Here we proceed as follows (i) (ii) Express the given series in the form Then the limit is its sum when n o = Lim f n) Replace by x, by dx and Lim the sign of n n o Tne lower and upper limits of integration will be the values offor the first and last term (or the limit of these values) respectively. (ii) when r= 0 x == 0 n -15X==1-1-1-0 n -1 n n - 1 n-1 Note In] f(a + rh) =In f(a +rh) r = 0 r= 0