Home
Class 12
MATHS
Let a(1),a(2),a(n) be sequence of real n...

Let `a_(1),a_(2),a_(n)` be sequence of real numbers with `a_(n+1)=a_(n)+sqrt(1+a_(n)^(2))` and `a_(0)=0`. Prove that `lim_(xtooo)((a_(n))/(2^(n-1)))=2/(pi)`

Text Solution

Verified by Experts

The correct Answer is:
`=4/(pi)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|39 Videos

  • LIMITS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

  • LOGARITHM AND THEIR PROPERTIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

If a_(1), a_(2),….,a_(n) are n(gt1) real numbers, then

If a_(1)=5 and a_(n)=1+sqrt(a_(n-1)), find a_(3) .

Let a_(1),a_(2)…,a_(n) be a non-negative real numbers such that a_(1)+a_(2)+…+a_(n)=m and let S=sum_(iltj) a_(i)a_(j) , then

If a_(1), a_(2), . . . , a_(n) is a sequence of non-zero number which are in A.P., show that (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+. . . + (1)/(a_(n)a_(1))= (2)/(a_(1) + a_(n)) [(1)/(a_(1))+(1)/(a_(2))+. . . +(1)/(a_(n))]

Statement-1: 1^(3)+3^(3)+5^(3)+7^(3)+...+(2n-1)^(3)ltn^(4),n in N Statement-2: If a_(1),a_(2),a_(3),…,a_(n) are n distinct positive real numbers and mgt1 , then (a_(1)^(m)+a_(2)^(m)+...+a_(n)^(m))/(n)gt((a_(1)+a_(2)+...+a_(b))/(n))^(m)

If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in

Let a_(1),a_(2),.......,a_(n) be fixed real numbers and define a function f(x)=(x-a_(1))(x-a_(2)) ......(x-a_(n)) , what is lim f(x) ? For some anea_(1),a_(2),.........a_(n) , compute lim_(Xrarr1) f(x)

If a_(1),a_(2),a_(3),a_(4),,……, a_(n-1),a_(n) " are distinct non-zero real numbers such that " (a_(1)^(2) + a_(2)^(2) + a_(3)^(2) + …..+ a_(n-1)^(2))x^2 + 2 (a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) + ……+ a_(n-1) a_(n))x + (a_(2)^(2) +a_(3)^(2) + a_(4)^(2) +......+ a_(n)^(2)) le 0 " then " a_(1), a_(2), a_(3) ,....., a_(n-1), a_(n) are in

If A_(1), A_(2),..,A_(n) are any n events, then

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen