Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given, sum of first n natural numbers = `1/2n^2 + 1/2n`
Sum of natural numbers from 11 to 30
= Sum of first 30 natural numbers – Sum of first 10 natural numbers
= `[1/2(30)^2 + 1/2(30)] - [1/2(10)^2 + 1/2(10)]`
= `900/2 + 30/2 - 100/2 - 10/2` ...[Divide each term by 2]
= 450 + 15 – 50 – 5
= 410
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: 10a3b3c3
If 9 is added to a certain number, the result is 36. Find the number.
If 11 is subtracted from 4 times a number, the result is 89. Find the number.
The sum of three consecutive natural numbers is 114. Find the numbers.
Find two numbers such that one of them exceeds the other by 18 and their sum is 92.
Find two numbers such that one of them is five times the other and their difference is 132.
The sum of two consecutive even numbers is 74. Find the numbers.
A man is 4 times as old as his son. After 16 years he will be only twice as old as his son. Find their present ages.
If I spend f rupees from 100 rupees, the money left with me is ______ rupees.
If m is a whole number, then 2 m denotes a multiple of 2.
The diameter of a circle is a line which joins two points on the circle and also passed through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre.) Express the diameter of the circle (d) in terms of its radius (r).
The side length of the top of square table is x. The expression for perimeter is ______.
The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?
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 the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of table of 10.
If 
= 2x + 3, 
= `3/2x + 7` and 
= x – 3 then find the value of:
2
+ 
– 
