Let a= (x^ 2 +2 x+3 x R ) and b= _ a 1- ^ 2 then the value of _ r=0 ^ n a^ r b^ n-r
Mathematics · JEE Main · NTA Exams — Progression and Series
Let \(a=\min \left(x^{2}+2 x+3 x \in R\right) \text { and } b=\lim _{\Delta \rightarrow a} \frac{1-\cos \theta}{\theta^{2}}\) then the value of \(\sum_{r=0}^{n} a^{r} \cdot b^{n-r}\)
- \(4^{n+1}-1\)
- \(\frac{4^{n+1}-1}{2^{n}}\)
- \(\frac{4^{n+1}-1}{3 \cdot 2^{n}}\)
- none of these
Answer
(C) 4^ n+1 -1 3 2^ n
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- If a_ 1 b_ 1 c are in AP; b, c, d are in GP; c_ 1 d_ 1 e are in HP, then a_ 1 c_ 1 e are in
- k and d (d being variable) are the n th term and common difference of an A.P. respectively. If the…
- If the arithmetic Mean of two positive numbers a and b (a > b) is twice their geometric Mean, then a : b is
- Three numbers form an increasing GP. If the middle number is doubled, then the new numbers are in AP. The…
- If x , y , z are in A.P. and tan –1 x , tan –1 y and tan –1 z are also in A.P., then
- The sum of the series 1 1 2 3 4 + 1 2 3 4 5 + n-terms is,
- Sum of infinite terms of series 3+5 1 4 +7 1 4^ 2 + . is
- If S _ n = n P + n ( n -1) 2 Q , where S n denotes the sum of the first n terms of an A.P., then the common…
More Progression and Series questions · Browse all practice questions