Let Sn=1+2+3++n and Pn=(S2)/(S2-1)dot(S...

Let `S_n=1+2+3++n` and `P_n=(S_2)/(S_2-1)dot(S_3)/(S_3-1)dot(S_4)/(S_4-1)...(S_n)/(S_n-1)` Where `n in N ,(ngeq2)dot` Then `("lim")_(n→oo)P_n=______`

`1/3`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

SEQUENCE AND SERIES
VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|19 Videos
SEQUENCE AND SERIES
VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos
QUADRATIC EQUATIONS
VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|43 Videos
SOLUTION OF TRIANGLES
VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|9 Videos

Similar Questions

Explore conceptually related problems

Let S_(n)=1+2+3+...+n " and " P_(n)=(S_(2))/(S_(2)-1).(S_(3))/(S_(3)-1).(S_(4))/(S_(4)-1)...(S_(n))/(S_(n)-1) , where n inN,(nge2) Then underset(ntooo)limP_(n) =__________.

If s_n=(1-4/1)(1-4/9)(1-4/25)......(1-4/((2n-1)^2)), where n in N, then

Let S_n=1/1^2 + 1/2^2 + 1/3^2 +….. + 1/n^2 and T_n=2 -1/n , then :

If S_(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))/(n!) then lim_(n rarr infty) S_(n) is equal to

The value of lim_(n->oo)[(2n)/(2n^2-1)cos(n+1)/(2n-1)-n/(1-2n)dot(n(-1)^n)/(n^2+1)]i s 1 (b) -1 (c) 0 (d) none of these

If S_(n)=(1^(2)-1+1)(1!)+(2^(2)-2+1)(2!)+...+(n^(2)-n+1)(n!) , then S_(50)=

If S_(1), S_(2), S_(3),...,S_(n) are the sums of infinite geometric series, whose first terms are 1, 2, 3,.., n and whose common rations are (1)/(2), (1)/(3), (1)/(4),..., (1)/(n+1) respectively, then find the values of S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ...+ S_(2n-1)^(2) .

If S_(n)=1+1/2+1/3+…+1/n(ninN) , then prove that S_(1)+S_(2)+..+S_((n-1))=(nS((n))-n)or(nS((n-1))-n+1)

Let S_n=Sigma_(k=1)^(4n) (-1)^((k(k+1))/2)k^2 .Then S_n can take value (s)

If S_n denotes the sum of n terms of A.P., then S_(n+3)-3S_(n+2)+3S_(n+1)-S_n= (a) S_2-n b. S_(n+1) c. 3S_n d. 0

VK JAISWAL ENGLISH-SEQUENCE AND SERIES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)

Let Sn=1+2+3++n and Pn=(S2)/(S2-1)dot(S3)/(S3-1)dot(S4)/(S4-1)...(Sn)...
Text Solution
|
Let a,b,c,d be four distinct real number in A.P.Then the smallest posi...
Text Solution
|
The sum of all digits of n for which sum (r =1) ^(n ) r 2 ^(r ) = 2+2^...
Text Solution
|
If lim ( x to oo) (r +2)/(2 ^(r+1) r (r+1))=1/k, then k =
Text Solution
|
The value of sum (r =1) ^(oo) (8r)/(4r ^(4) +1) is equal to :
Text Solution
|
Three distinct non-zero real numbers form an A.P. and the squares of t...
Text Solution
|
which term of an AP is zero -48,-46,-44.......?
Text Solution
|
In an increasing sequence of four positive integers, the first 3 terms...
Text Solution
|
The limit of (1)/(n ^(4)) sum (k =1) ^(n) k (k +2) (k +4) as n to oo i...
Text Solution
|
Which is the last digit of 1+2+3+……+ n if the last digit of 1 ^(3) + ...
Text Solution
|
There distinct positive numbers, a,b,c are in G.P. while log (c) a, lo...
Text Solution
|
The numbers 1/3, 1/3 log (x) y, 1/3 log (y) z, 1/7 log (x) x are in H...
Text Solution
|
If sum ( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relativel...
Text Solution
|
The sum of the terms of an infinitely decreassing Geometric Progressio...
Text Solution
|
A cricketer has to score 4500 runs. Let a (n) denotes the number of ru...
Text Solution
|
If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...
Text Solution
|
Let f (n)=(4n + sqrt(4n ^(2) -1))/( sqrt(2n +1 )+sqrt(2n-1)),n in N th...
Text Solution
|
Find the sum of series 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+…… oo, where the...
Text Solution
|
Let a (1), a(2), a(3),…….., a(n) be real numbers in arithmatic progres...
Text Solution
|
Let the roots of the equation 24 x ^(3) -14x ^(2) + kx +3=0 form a geo...
Text Solution
|
How many ordered pair (s) satisfy log (x ^(3) + (1)/(3) y ^(3) + (1)/(...
Text Solution
|