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")_(xvecoo)P_n=______`

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) =__________.

Let p_n=a^(P_(n-1))-1,AAn=2,3, ,a n dl e tP_1=a^x-1, where a in R^+dot Then evaluate ("lim")_(xvec0)(P_n)/x

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+a_1+a_2+a_3++a_n ,a_1 in R^+ for i=1ton , then prove that S/(S-a_1)+S/(S-a_2)++S/(S-a_n)geq(n^2)/(n-1),AAngeq2

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

The absolute value of the sum of first 20 terms of series, if S_(n)=(n+1)/(2) and (T_(n-1))/(T_(n))=(1)/(n^(2))-1 , where n is odd, given S_(n) and T_(n) denotes sum of first n terms and n^(th) terms of the series

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) .

Let S_(1), S_(2), ...... S_(101) be consecutive terms of A.P. If 1/(S_(1)S_(2)) + 1/(S_(2)S_(3)) + ...... + 1/(S_(100)S_(101)) = 1/6 and S_(1) + S_(101) = 50 , then |S_(1) - S_(101)| is equal to

If S_n denotes the sum of first n terms of an A.P. and (S_(3n)-S_(n-1))/(S_(2n)-S_(2n-1))=31 , then the value of n is 21 b. 15 c.16 d. 19

Let s_(n) denote the sum of first n terms of an A.P. and S_(2n) = 3S_(n) . If S_(3n) = kS_(n) then the value of k is equal to