NCERT Solutions For Class 11 Maths chapter-9 Sequences And Series Exercise 9.4

NCERT Solutions for Class-11 Maths Chapter-9 Sequences and Series

NCERT Solutions For Class 11 Maths Chapter-9 Sequences and Series Exercise 9.4 prepared by the expert of Physics Wallah score more with Physics Wallah NCERT Class 11 maths solutions. You can download solution of all chapters from Physics Wallah NCERT solutions of class 11.

 

NCERT Solutions for Class-11 Maths Exercise 9.4

 

Find the sum to n terms in each of the series in Exercises 1 to 7.

 

Question1. Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 +...

Solution :
Given:1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 +...to n^th terms

The n^th term of the series is a_n = n(n+1)

 

Question2. Find the sum to n terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

 Solution :
 

a_n =n(n+1)(n+2)

=(n² + n)(n + 2)

=n³ + 3n² + 2n
The sum of n terms of a series is given by the equation

=

Question3. Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7×3²+…

 Solution :
Given: 3 × 1² + 5 × 2² + 7×3²+…to   n^th terms

 

Question4.

Solution :
Given: to n^th terms

 

Question5. Find the sum to n terms of the series 5² + 6² + 7²+…+20²

 Solution :
 

Given: 5² + 6² + 7²+…+20²

= The n^th term of the series is

= an=(n+4)²

=n²+8n+16

= The sum of n terms of a series is given by the equation

=

 

Question6. Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 + …

 Solution :
Given: 3 × 8 + 6 × 11 + 9 × 14 + …to n^th terms

an= (nth
term of 3,6,9...
)×
(nth
term of 8,11,14...

)

=(3n)(3n+5)

=9n2+15n

The sum of n terms of a series is given by the equation

 The sum of  n terms of the given series is
 .

 

Question7. Find the sum to n terms of the series 1² + (1² + 2²) + (1² + 2² + 3²)+…

 Solution :
Given: 1² + (1² + 2²) + (1² + 2² + 3²)+…to n^th terms

Find the sum to n terms in each of the series in Exercises 8 to 10 whose nth terms is given by

Question8. Find the sum to n terms of the series n(n+1)(n+4)

 Solution :
Given:n(n+1)(n+4)

 

Question9. n²+2ⁿ

Solution :
Given:n²+2ⁿ

The nth term of the series is an = n²+2n

The sum of n terms of a series is given by the equation

The sum of first n terms of the given series is

 

Question10. Find the sum to n terms of the series  (2n−1)²

 Solution :
Given:(2n−1)²

the n^th term of the series is an=(2n−1)²

=4n²−4n+1The sum of n terms of a series is given by the equation

 .The sum of first  n^th  terms of the given series is