Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 53)
53.
(112 + 122 + 132 + ... + 202) = ?
Answer: Option
Explanation:
(112 + 122 + 132 + ... + 202) = (12 + 22 + 32 + ... + 202) - (12 + 22 + 32 + ... + 102)
 |
Ref: (12 + 22 + 32 + ... + n2) = | 1 | n(n + 1)(2n + 1) |  |
|
| 6 |
| = |  |
20 x 21 x 41 | - | 10 x 11 x 21 |  |
| 6 | 6 |
= (2870 - 385)
= 2485.
Discussion:
33 comments Page 1 of 4.
J shivani said:
5 years ago
Here, we use n[n+1][2n+1]/6.
Here we take n=20 then substitute we get 2870
Next we have to take n=10 then substitute we get 385
Later Subtract 2870-385=2485.
It is bcoz in n=20 we are considering squares from 1 to 20 but it is from 11 to 20.
So, t n=20 then the sum of 1 to 20 is subtracted.
Here we take n=20 then substitute we get 2870
Next we have to take n=10 then substitute we get 385
Later Subtract 2870-385=2485.
It is bcoz in n=20 we are considering squares from 1 to 20 but it is from 11 to 20.
So, t n=20 then the sum of 1 to 20 is subtracted.
(8)
Sagar jeevtani said:
5 years ago
@All.
To find the sum of (square of natural numbers) we can use the formula that is.
sn=n (n+1) (2n+1) /6 upto n terms.
But here,We have to find the sum of the square of a natural number between 11 to 20 then we have to subtract the sum of the square of natural number from 1 to 10 then we can get the answer.
To find the sum of (square of natural numbers) we can use the formula that is.
sn=n (n+1) (2n+1) /6 upto n terms.
But here,We have to find the sum of the square of a natural number between 11 to 20 then we have to subtract the sum of the square of natural number from 1 to 10 then we can get the answer.
(3)
Gauri Sharma said:
5 years ago
I didn't got it. Please explain.
(2)
Ruchita said:
6 years ago
Can anyone explain me formula?
I don't want to remember it but I want to understand it.
I want to understand formula like why we have to divide 6 in this formula?
I don't want to remember it but I want to understand it.
I want to understand formula like why we have to divide 6 in this formula?
VARSHA said:
6 years ago
Sn = S20 - S10.
S10 = (1/6)(n(n+1)(2n+1)
= (10*11*21)/6 =385.
S20 = (1/6)(n(n+1)(2n+1)
= (20*21*41)/6 = 2870.
Sn = S20-S10.
= 2870-385,
= 2485.
S10 = (1/6)(n(n+1)(2n+1)
= (10*11*21)/6 =385.
S20 = (1/6)(n(n+1)(2n+1)
= (20*21*41)/6 = 2870.
Sn = S20-S10.
= 2870-385,
= 2485.
(3)
Sruthi said:
7 years ago
By applying n(n+1)(2n+1)/6 we get the answer directly.
Hence given upto 20.
So, here n=20.i.e.20(21)(41)/6=2870.
Hence given upto 20.
So, here n=20.i.e.20(21)(41)/6=2870.
(2)
Gowry said:
7 years ago
It is very simple.
We can learn squares to addition.
121+144+169+196+225+256+289+324+361+400 = 2485.
But it is below 20^2.
We can learn squares to addition.
121+144+169+196+225+256+289+324+361+400 = 2485.
But it is below 20^2.
(2)
Nithish said:
7 years ago
How did ^66 Came? I didn't understand.
Tharakesh said:
7 years ago
Here, (1**2+2**2+3**2+.........+n**2) = (1/6)(n(n+1)(2n+1)
n=20.
(1/6)(20*21*41)=2870.
n=20.
(1/6)(20*21*41)=2870.
(1)
Venkat said:
7 years ago
I can't understand. Please help me to get it.
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