सिद्ध कीजिए की
` (1)/(|__1) +(1+a)/(|__2) +( 1+a+ a^(2))/( |__3) +.............= ( e ^(a) -e)/( a-1) ,agt1 `

सिद्ध कीजिए कि 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

(1) / (log_ (3) e) + (1) / (log_ (3) e ^ (2)) + (1) / (log_ (3) e ^ (4)) + ... =

Value of lim_(a to oo) (e.a^(2).e^(3).a^(4). ..........e^(n-1)a^(n))^((1)/(n^(2)+1)) is

Show that 1+(1+3)/(2!)+(1+3+3^2)/(3!)+...=1/2(e^3-e)

Let E=(1)/(1^(2))+(1)/(2^(2))+(1)/(3^(2))+ Then,a.E 3/2c.E>2d.E<2

if cos (1-i) = a+ib, where a , b in R and i = sqrt(-1) , then a. a = (1)/(2)(e-(1)/(e))cos 1, b = (1)/(2)(e+(1)/(e))sin 1 b. a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1 c. a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e+(1)/(e))sin 1 d. a=(1)/(2)(e-(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1

The value of lim_(x->0)((1+2x)/(1+3x))^(1/x^2)e^(1/x) is e^(5/2) b. e^2 c. e^(-2) d. 1