Sigma n2

Q.

Find the sum of the series 0.6 + 0.66 + 0.666 + ... .

Or

The product of the three numbers in GP is 216. If 2, 8 and 6 be added to them, then the results are in Al, find the numbers.

Q.

If a, b, c are distinct positive numbers, then the expression (b + c - a) (c + a - b) (a + b - c) - abc

1. non-positive

2. Positive

3. negative

4. non-negative

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. All of these

4. 

Q.

Differentiate $\left(\frac{x^2+5x-6}{4x^2-x+3}\right)$

Q.

Find the next term in the series $2,3,8,63$.

Q.

Find the derivative of $x^n+a{x}^{n-1}+a^2{x}^n-2+...+a^{n-1}x+a^n$ for some fixed real number a.

Q. Find the sum to n terms of each of the series in Exercises 1 to 7 1: 1x2+2x3+3 x4 4 x5+2. 1 x2 x 3+2 x3 4+34 3. 3 x 1 +5 x 22 +7 x3 +... 5. 5+6+72 + 20 Ix2 2x3 3x4 3x8+6x11+9x14 + 6,

Q.

Find the value of $\frac{{1.2}^2+{2.3}^2+{3.4}^2+-------nterms}{1^2.2+2^2.3+3^2.4+-------nterms}$.

1. 

2. 

3. 

4. 

Q.

$1^3+2^3+3^3+\cdots +n^3={\left[\frac{n(n+1)}{2}\right]}^2$

Q.

Find the sum to n terms of the series whose nth term is given by

$n(n+1)(n+4)$

Q.

The sum of i - 2 - 3i + 4 + ....... upto 100 terms, which i = $\sqrt{-1}$

is

1. 100(1-i)

2. 50(1-i)

3. 25i

4. 25(1+i)

Q.

$1.2+{2.2}^2+{3.2}^3+\cdots +n.2^n=(n-1)2^{n+1}+2.$

Q.

The sum of first n terms of the given series $1^2+{2.2}^2+3^2+{2.4}^2+5^2+{2.6}^2+.........is\frac{n(n+1{)}^2}{2}$, When n is even. When n is odd, the sum will be

1. 

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.

Prove $1^2+3^2+5^2+\cdots +(2n-1{)}^2=\frac{n(2n-1)(2n+1)}{3}$

Q. The sum of first n terms of the series $1^2+2\times 2^2+3^2+2\times 4^2+5^2+2\times 6^2+.....$ is $\frac{n(n+1{)}^2}{2}$ when $n$ is even. When $n$ is odd the sum of the series is

1. $\frac{n^2(n+1)}{2}$
2. None of these.
3. $\frac{n^3(n-1)}{2}$
4. $\frac{n^2(3n+1)}{4}$

Q.

Find the sum to ${}^{\prime }{n}^{\prime }$ terms of the series

$5^2+6^2+7^2+.........+{20}^2$

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. ${tan}^{-1}$( $\frac{n}{n+2}$)

2. ${cot}^{-1}$( $\frac{n+2}{n}$)

3. ${tan}^{-1}$(n+1) - ${tan}^{-1}$ 1

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

Q. 5. 52 + 62 7.202

Q.

Find the sum to n terms

$3\times 1^2+5\times 2^2+7\times 3^2+\dots \dots$

Q.

If 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. $\frac{n(4n^2-1)}{3}{C}^2$

2. $\frac{n(4n^2-1)}{6}{C}^2$

3. $\frac{n(4n^2-1)}{3}{C}^2$

4. $\frac{n(4n^2+1)}{6}{C}^2$

Q.

Find the sum of the series $4+4^2+4^3+...{.4}^{100}+{4.4}^{101}$

1. 

2. 

3. 

4. 

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 sum to $n$ terms of the sequence $8,88,888,8888,....$ .

Q. 7. 12(12(122232) +

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, $\frac{1}{2}$

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.

Which term in the A.P 7, 3, 1.................. is -73?

__