Let a1,a2,.........an be real numbers ...

Let `a_1,a_2,.........a_n` be real numbers such that `sqrt(a_1)+sqrt(a_2-1)+sqrt(a_3-2)++sqrt(a_n-(n-1))=1/2(a_1+a_2+.......+a_n)-(n(n-3)/4` then find the value of `sum_(i=1)^100 a_i`

Text Solution

AI Generated Solution

Topper's Solved these Questions

RELATIONS AND FUNCTIONS
CENGAGE ENGLISH|Exercise All Questions|9 Videos
STRAIGHT LINES
CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n

Let a_1, a_2, a_3, ...a_(n) be an AP. then: 1 / (a_1 a_n) + 1 / (a_2 a_(n-1)) + 1 /(a_3a_(n-2))+......+ 1 /(a_(n) a_1) =

If a_1,a_2,a_3, ,a_n are an A.P. of non-zero terms, prove that 1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)= (n-1)/(a_1a_n)

If a_1,a_2,a_3,....a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1+a_2+.......a_(n-1)+2a_n is

If a_r>0, r in N and a_1.a_2,....a_(2n) are in A.P then (a_1+a_2)/(sqrta_1+sqrta_2)+(a_2+a_(2n-1))/(sqrta_2+sqrta_3)+.....+(a_n+a_(n+1))/(sqrt a_n+sqrta_(n+1))=

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)_(x->a_1)f(x) ? For some a!=a_1,a_2,.....,a_n , compute (lim)_(x->a)f(x)

If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_2)+sqrt(a_3))+ ..+1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_2)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions

Find the sum of n terms of the series whose nth term is T(n)=tanx/(2^n...
Text Solution
|
The value of sum(i=0)^oosum(j=0)^oosum(k=0)^oo1/(3^i3^j3^k) is
Text Solution
|
Let a1,a2,.........an be real numbers such that sqrt(a1)+sqrt(a2-1)+...
Text Solution
|
If log(2)(5xx2^(x)+1),log(4)(2^(1-x)+1) and 1 are in A.P., then x equa...
Text Solution
|
Let S(k), where k = 1,2,....,100, denotes the sum of the infinite geom...
Text Solution
|
If x=sum(n=0)^oocos^(2n)theta,y=sum(n=0)^oosin^(2n)varphi,z=sum(n=0)^o...
Text Solution
|
The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...
Text Solution
|
Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...
Text Solution
|
The sum of the first three terms of a strictly increasing G.P. is alph...
Text Solution
|
If (log)3 2,(log)3(2^x-5) and (log)3(2^x-7/2) are in arithmetic progre...
Text Solution
|
If p is the first of the n arithmetic means between two numbers and q ...
Text Solution
|
If S1, S2 ,S3,.........Sn,........ are the sums of infinite geometri...
Text Solution
|
The interior angles of a polygon are in arithmetic progression. The sm...
Text Solution
|
If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/(sqr...
Text Solution
|
How many geometric progressions are possible containing 27, 8 and 12 a...
Text Solution
|
Find three numbers a,b,c between 2 & 18 such that; their sum is 25; th...
Text Solution
|
Find the sum 1+2(1+1/50)+3(1+1/50)^(2)+…50 terms.
Text Solution
|
The sum of 50 terms of the series 3/(1^2)+5/(1^2+2^2)+7/(1^2+2^2+3^2)+...
Text Solution
|
If a1, a2, an are in A.P. with common difference d!=0 , then the sum ...
Text Solution
|
The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...
Text Solution
|