Home
Class 11
MATHS
If S1, S2,S3,S4,.....,Sp denotes the su...

If `S_1, S_2,S_3,S_4,.....,S_p ` denotes the sums of infinite geometric series whose first terms are 1, 2, 3,...p respectively and whose common ratios are `1/2,1/3,1/4,.....1/(p+1) ` respectively .then `S_1+S_2+S_3+....+S_p` = kp(p+3), where k =?

Promotional Banner

Similar Questions

Explore conceptually related problems

If S_1, S_2, S_3,…..S_p are the sum of infinite geometric series whose first terms are 1,2,3,…p and whose common ratios are 1/2,1/3,1/4,….1/(p+1) respectively, prove that S_1+S_2+……..+S_p=p(p+3)/2

If S_(1),S_(2), S_(3),......, S_(p) are the sums of infinite geometric series whose first terms are 1, 2, 3..... p and whose common ratios are (1)/(2),(1)/(3),.... (1)/(p+1) respectively, prove that S_(1) +S_(2)+S_(3)+.... + S_(p) = (1)/(2) p (p+3) .

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_(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_(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_(1), S_(2), S_(3),…., S_(n) are the sums to infinity of n infinte geometric series whose first terms are 1,2,3,… n and whose common ratios are (1)/(2), (1)/(3), (1)/(4), ….(1)/(n+1) respectively, show that, S_(1) + S_(2) + S_(3) +…S_(n) = (1)/(2)n(n+3)

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 ratio 1/2,1/3,1/4,........,1/(n+1),....respectively, then find the value of sum_(r=1)^(2n-1) S_1^2.

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 ratio 1/2,1/3,1/4,........,1/(n+1),.... respectively, then find the value of sum_(r=1)^(2n-1) S_1^2 .