Home
Class 11
MATHS
S(n+3) - 3S(n+2) +3S(n+1) - S(n) = 0...

`S_(n+3) - 3S_(n+2) +3S_(n+1) - S_(n)` = 0

Text Solution

Verified by Experts

Given
=`S_(n+3) - 3S_(n+2) +3S_(n+1) - S_(n)` = 0
=`(S_(n+3)-S_(n+2))-2(S_(n+2)+S_(n+1))+(S_(n+1)-S_(n))`
=`T_(n+3)-2T_(n+2)+T_(n+1)`
=`T_(n+3)-2((T_(n+1)+T_(n+3))/2)+T_(n+1)`
=`T_(n+3)+T_(n+1)-T_(n+1)-T_(n+3)`
=`0`=R.H.S
Promotional Banner

Similar Questions

Explore conceptually related problems

If S_(n) denotes the sum of n terms of an A.P., S_(n +3) - 3S_(n + 2) + 3S_(n + 1) - S_(n) =

If S_(n) danotes the sum of n terms of n terms of an A.P. then S_(n + 3) - 3 S_(n + 2) + 3S_(n + 1) - S_(n) =

If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+4) - 4S_(n+3) + 6S_(n+2) -4S_(n+1) +S_(n) = 0

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

Let S_(n) denote the sum of the first n terms of an A.P. If S_(2n) = 3S_(n) , then S_(3n) : S_(n) is equal to :

If S_(n), denotes the sum of n terms of an A.P. then S_(n+3)-3S_(n+2)+3S_(n+1)-S_(n)=

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

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).2^S_n b). s_(n+1) c). 3S_n d). 0

If S_(n) denotes the sum of n terms of A.P.then S_(n+1)-3S_(n+2)+3S_(n+1)-S_(n)=2^(S)-nbs_(n+1)c.3S_(n)d.0

If S_(1), S_(2), S_(3) be respectively the sums of n, 2n and 3n terms of a G.P., prove that, S_(1)(S_(3) - S_(2)) = (S_(2) - S_(1))^(2) .