(asin sum_(x=1)^(n)sqrt(x)sum_(x=1)^(n)(1)/(sqrt(x)))/(sum_(x=1)^(n)x)

sum_(n=1)^(oo)(1)/(sqrt(n)+sqrt(n+1))

Let x_(1),x_(2),x_(n) be n observations and X be their arithmetic mean.The standard mean is given by sum_(i=1)^(n)(x_(i)-X)^(2) (b) (1)/(n)sum_(i=1)^(n)(x_(i)-X)^(2) (c) sqrt((1)/(n)sum_(i=1)^(n)(x_(i)-X)^(2))( c) (1)/(n)sum_(i=1)^(n)xi2-X^(2)

The mean deviation for n observations x_(1),x_(2),.........,x_(n) from their mean X is given by (a)sum_(i=1)^(n)(x_(i)-X)(b)(1)/(n)sum_(i=1)^(n)(x_(i)-X)(c)sum_(i=1)^(n)(x_(i)-X)^(2)(c)(1)/(n)sum_(i=1)^(n)(x_(i)-X)^(2)

The mean deviation for n observations x_(1),x_(2)…….x_(n) from their median M is given by (i) sum_(i=1)^(n)(x_(i)-M) (ii) (1)/(n)sum_(i=1)^(n)|x_(i)-M| (iii) (1)/(n)sum_(i=1)^(n)(x_(i)-M)^(2) (iv) (1)/(n)sum_(i=1)^(n)(x_(i)-M)

Prove that identity : sum_(i=1)^(n) (x_i-bar x)^2 = sum_(i=1)^(n) x_i^2-n bar x^2= sum_(i=1)^(n) x_i^2 -(sum_(i=1)^(n) x_i)^2/n .

lim_(x rarr2)(sum_(r=1)^(n)x^(r)-sum_(r=1)^(n)2^(r))/(x-2)

If sum_(i=1)^(n)sin x_(i)=n then sum_(i=1)^(n)cot x_(i)=

If sum_(i=1)^(n)sin x_(i)=n then sum_(i=1)^(n)cot x_(i)=

If the sum of the series sum_(n=1)^(oo)((sec^(-1)sqrt(|x|)+cosec^(-1)sqrt(|x|))/(pi a))^n is finite where |x|>=1 and a>0 then range of values of a

If the sum of the series sum_(n=1)^(oo)((sec^(-1)sqrt(|x|)+cosec^(-1)sqrt(|x|))/(pi a))^n is finite where |x|>=1 and a>0 then range of values of a