VN Method

Q.

$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\dots .+\frac{1}{n(n+1)}equals$

1. $\frac{1}{n(n+1)}$

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

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

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

Q. Statement - 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16)+...+(361 + 380 + 400) is 8000.
Statement - 2: ${\sum }_{k=1}^n(k^3-(k-1{)}^3)=n^3,$ for any natural number n.

1. Statement - 1 is false, Statement - 2 is true.
2. Statement - 1 is true, Statement - 2 is true, Statement - 2 is a correct explanation for Statement - 1.
3. Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation for Statement - 1.
4. Statement - 1 is true, Statement - 2 is false.

Q. The sum 1(1!) + 2(2!) + 3(3!) + ....+n (n!) equals

[AMU 1999; DCE 2005]

1. 3(n!) + n - 3
2. (n + 1)! - (n - 1)!
3. (n + 1)! - 1
4. 2(n!) - 2n - 1

Q. $\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+....\frac{1}{n(n+1)}$ equals
[AMU 1995; RPET 1996; UPSEAT 1999, 2001]

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

Q.

The sum of $(n+1$) terms of $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+......$ is

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

Q.

Find the value of $\left(\frac{4}{5}\mathrm{of}500\right)-320$

Q.

Find the sum upto first 11 terms of the series 1.4.7 + 4.7.10 + 7.10.13 + . . . . . is___