Advertisements
Advertisements
प्रश्न
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 11 natural numbers.
Advertisements
उत्तर
Given, sum of first n natural numbers = `1/2n^2 + 1/2n`
Sum of first 11 natural numbers = `1/2(11)^2 + 1/2(11)` ...[Put n = 11]
= `1/2 xx 121 + 11/2`
= `121/2 + 11/2`
= `132/2`
= 66
APPEARS IN
संबंधित प्रश्न
Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.
If the number of digits formed is taken to be n, the number of segments required to
form n digits is given by the algebraic expression appearing on the right of each pattern.
How many segments are required to form 5, 10, 100 digits of the kind −
Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.
If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.
How many segments are required to form 5, 10, 100 digits of the kind −
Write down the following in the product form: x2y4
If 9 is added to a certain number, the result is 36. Find the number.
Find a number which when multiplied by 5 is increased by 80.
The sum of two consecutive even numbers is 74. Find the numbers.
Deepak is twice as old as his brother Vikas. If the difference between their ages is 11 years, find their present ages.
If x is a negative integer, – x is a positive integer.
The side of an equilateral triangle is shown by l. Express the perimeter of the equilateral triangle using l.
A cube is a three-dimensional figure as shown in the given figure. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.
To find sum of three numbers 14, 27 and 13, we can have two ways:
- We may first add 14 and 27 to get 41 and then add 13 to it to get the total sum 54 or
- We may add 27 and 13 to get 40 and then add 14 to get the sum 54. Thus, (14 + 27) + 13 = 14 + (27 + 13)
This can be done for any three numbers. This property is known as the associativity of addition of numbers. Express this property which we have already studied in the chapter on whole numbers, in a general way, by using variables a, b and c.
The side length of the top of square table is x. The expression for perimeter is ______.
In a rectangular plot, 5 square flower beds of side (x + 2) metres each have been laid (see the figure). Find the total cost of fencing the flower beds at the cost of ₹ 50 per 100 metres:
A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions:
- How much wire is left?
- If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 5 natural numbers.
The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of table of 10.
The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of table of 19.
If 
= 2x + 3, 
= `3/2x + 7` and 
= x – 3 then find the value of:
`1/2`
+ 
– 3
If 
= `3/4x - 2` and 
= x + 6, then find the value of:
– 
