# Chapter 9 Sequences and Series Ex – 9.4

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

Question 1.

1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ………

Solution:

In the given series, there is a sum of multiple corresponding terms of two A.P’s. The two A.P’s are

Question 2.

1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ……

Solution:

In the given series, there is a sum of multiple of corresponding terms of two A.P’s. The three A.P’s are Question 3.

3 x 12 + 5 x 22 + 7 x 32 + …..

Solution:

In the given series there is sum of multiple of corresponding terms of two A.P’s. The two A.P’s are

(i) 3, 5, 7, …………… and

(ii) 12, 22, 32, ………………….

Now the nth term of sum is an = (nth term of the sequence formed by first A.P.) x (nth term of the sequence formed by second A.P.) = (2 n + 1) x n2 = 2n3 + n2 Hence, the sum to n terms is,

Question 4. $\frac { 1 }{ 1\times 2 } +\frac { 1 }{ 2\times 3 } +\frac { 1 }{ 3\times 4 } +$ …….

Solution:

In the given series there is sum of multiple of corresponding terms of two A.P’s. The two A.P’s are

Question 5.

52 + 62 + 72 + ………….. + 202

Solution:

The given series can be written in the following way

Question 6.

3 x 8 + 6 x 11 + 9 x 25 + ………….

Solution:

In the given series, there is sum of multiple of corresponding terms of two A.P/s. The two A.P/s are

(i) 3, 6, 9, ………….. and

(ii) 8, 11, 14, ……………….

Now the nth term of sum is an = (nth term of the sequence formed by first A.P.) x (nth term of the sequence formed by second A.P.)

Question 7.

12 + (12 + 22) + (12 + 22 + 32) + ………….

Solution:

In the given series

an = 12 + 22 + …………….. + n2

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

Question 8.

n(n + 1)(n + 4)

Solution:

We have

Question 9.

n2 + 2n

Solution:

We have an = n2 + 2n

Hence, the sum to n terms is,

Question 10.

(2n – 1)2

Solution:

We have