Sum of first n terms in the following series c o t − 1 3 + c o t − 1 7 + c o t − 1 13 + c o t − 1 21 + .........n terms.is given by Options: A . &nbsptan−1( nn+2) B . &nbspcot−1( n+2n) C . &nbsptan−1(n+1) - tan−1 1 D . &nbspAll of these

Sum of first n terms in the following series cot−13 + cot−1

Question

Sum of first n terms in the following series

{c o t}^{- 1}

3 +

{c o t}^{- 1}

7 +

{c o t}^{- 1}

13 +

{c o t}^{- 1}

21 + .........n terms.is given by

Options:

A . tan−1( nn+2)

B . cot−1( n+2n)

C . tan−1(n+1) - tan−1 1

D . All of these

Answer: Option D
:
D
Let S = 3 + 7 + 13 + 21 + ...... +

T_{π}

⇒

T_{π}

n^{2}

+ n + 1.
Let

T_{r}

{c o t}^{- 1}

(

r^{2}

+ r + 1) =

{t a n}^{- 1}

(r + 1) -

{t a n}^{- 1}

r.
Put r = 1, 2,........, n and add, we get the required sum

{t a n}^{- 1}

(n+1) -

{t a n}^{- 1}

1 =

{t a n}^{- 1}

(

\frac{n}{n + 2}

) =

{c o t}^{- 1}

(

\frac{n + 2}{n}

)

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If sixth term of a H.P. is 161 and its tenth term is 1105, then first term of that H.P. is....

Question 2. The sum of infinite terms of the following series 1 + 45 + 752 + 1053 + ...........∞ ....the following series 1 + 45 + 752 + 1053 + ...........∞ will be

Question 3. Harikiran purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual instalment o....interest. How much money is to be paid by him

Question 4. The sum of the first n terms is 12 + 34 + 78 + 1516 + .......... is....

Question 5. If the aritmetic, geometric and harmonic menas between two positive real numbers be A, G and H, then....

Question 6. If p, q, r are in A.P. and are positive, the roots of the quadratic equation p x2 + qx + r = 0 are all real for ___.....

Question 7. If m≠n and the sequences p,a,b,q and p,m,n,q each are in AP, then b−an−m is ___.....

Question 8. Let {an} be a non - constant arithmetic progression with a1=1 and for any n≥1, the value a2n+a2n−1+Ȯ....and for any n≥1, the value a2n+a2n−1+⋯+an+1an+an−1+⋯a1 remains constant. Then, a15 will be?

Question 9. 214. 418. 8116. 16132................ is equal to....

Question 10. If the aritmetic, geometric and harmonic menas between two positive real numbers be A, G and H, then ....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers