Advertisements
Advertisements
Question
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 5 natural numbers.
Advertisements
Solution
Given, sum of first n natural numbers = `1/2n^2 + 1/2n`
Sum of first 5 natural numbers = `1/2(5)^2 + 1/2(5)` ...[Put n = 5]
= `25/2 + 5/2`
= `30/2`
= 15
APPEARS IN
RELATED QUESTIONS
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
Write down the following in the product form: 6y5
If 9 is added to a certain number, the result is 36. Find the number.
Find two numbers such that one of them is five times the other and their difference is 132.
Reena is 6 years older than her brother Ajay. If the sum of their ages is 28 years, what are their present ages?
Mrs. Goel is 27 years older than her daughter Rekha. After 8 years she will be twice as old as Rekha. Find their present ages.
The area of a square having each side x is ______.
The additive inverse of an integer x is 2x.
The side of an equilateral triangle is shown by l. Express the perimeter of the equilateral triangle using l.
The side of a regular hexagon is denoted by l. Express the perimeter of the hexagon using l.
(Hint: A regular hexagon has all its six sides equal in length.)
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 sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 11 natural numbers.
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of natural numbers from 11 to 30.
Write an expression for the sum of 1 and twice a number n. If you let n be any odd number, will the result always be an odd number?
