Advertisements
Advertisements
प्रश्न
The sum of squares of first n natural numbers is given by `1/6n(n + 1)(2n + 1)` or `1/6(2n^3 + 3n^2 + n)`. Find the sum of squares of the first 10 natural numbers.
Advertisements
उत्तर
Given, the sum of squares of first n natural numbers = `1/6(n +1)(2n + 1)`
∴ The sum of squares of first 10 natural numbers ...[∴ Put n = 10]
= `1/6 (10)(10 + 1)(2 xx 10+1)`
= `1/6 xx 10 xx 11 xx 21`
= 385
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 −
Write down the following in the product form: 9xy2z
Find a number which when multiplied by 5 is increased by 80.
When Raju multiplies a certain number by 17 and adds 4 to the product, he gets 225. Find that number.
Find two numbers such that one of them exceeds the other by 18 and their sum is 92.
One out of two numbers is thrice the other. If their sum is 124, find the numbers.
The sum of two consecutive even numbers is 74. Find the numbers.
Reena is 6 years older than her brother Ajay. If the sum of their ages is 28 years, what are their present ages?
The area of a square having each side x is ______.
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?
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:
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:
2
+ 
– 
If 
= `3/4x - 2` and 
= x + 6, then find the value of:
– 
