Sigma n2

Q.

The sum of n terms of the series whose $n^{th}$ term is n(n+1) is equal to

1. 

2. 

3. 

4. 

Q.

The value of the series $\left(\frac{1^1}{2}\right)+\left(\frac{1^2+2^2}{3}\right)+\left(\frac{1^2+2^2+3^2}{4}\right)+.....$ is

1. $\frac{n(n+1)(4n+5)}{36}$
   

2. $\frac{n(n-1)(4n+5)}{6}$
   

3. $\frac{n(n+1)(4n+2)}{3}$
   

4. None of these
   

Q. In the sum of first n terms of an A.P. is $c{n}^2$. then the sum of squares of these n terms is

1. $\frac{n(4n^2+1)c^2}{3}$
2. $\frac{n(4n^2-1)c^2}{6}$
3. $\frac{n(4n^2-1)c^2}{3}$
4. $\frac{n(4n^2+1)c^2}{6}$

Q.

Sum of first n terms in the following series

${cot}^{-1}$3 + ${cot}^{-1}$7 + ${cot}^{-1}$13 + ${cot}^{-1}$21 + .........n terms.is given by

1. 

2. 

3. 

4. All of these

Q. If the sum of the first ten terms of the series
${\left(1\frac{3}{5}\right)}^2+{\left(2\frac{2}{5}\right)}^2+{\left(3\frac{1}{5}\right)}^2+4^2+{\left(4\frac{4}{5}\right)}^2+\dots \dots is\frac{16}{5}m$, then m is equal to

1. 102
2. 101
3. 100
4. 99

Q.

Find the sum of the series $2^2$ + $4^2$ + $6^2$ + $8^2$ +................ 20 terms __

Q. If the sum of the first ten terms of the series ${\left(1\frac{3}{5}\right)}^2+{\left(2\frac{2}{5}\right)}^2+{\left(3\frac{1}{5}\right)}^2+4^2+{\left(4\frac{4}{5}\right)}^2+.....,$is $\frac{16}{5}m,$ then m is equal to:

1. 99
2. 102
3. 101
4. 100

Q.

Harikiran purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual instalment of Rs. 1000 with 10% per annum interest. How much money is to be paid by him

1. Rs. 20475

2. Rs. 20500

3. Rs. 20700

4. Rs. 21555

Q.

Find the ${20}^{th}$ term and sum of the 20 term of the series 1, 4, 7, 10....

1. 58, 490

2. 59, 590

3. 59, 490

4. 58, 590

Q.

Find the sum of the products of the corresponding terms of finite geometrical progressions

2, 4, 8, 16, 32 and 128, 32, 8, 2, $\frac{1}{2}$