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 2 of 4.
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?
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)
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)
Bijoy said:
1 decade ago
Where did we get the value of {n(n+1)(2n+1)}/6 from?
Can someone help please in simple way?
Can someone help please in simple way?
Kavitha chowdary said:
1 decade ago
According to the formula the answer is 2870. But why we subtract 385? Anyone please tell me.
Sumedha said:
9 years ago
I didn't get a proper answer. Please, can anybody give me proper answer & shortcut.
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)
Rajni Saini said:
1 decade ago
I can't understand, can you give any shortcut method to solve this problem plzzzz.
Inder said:
10 years ago
From where this come from (12 + 22 + 32 +.....+ 202) - (12 + 22 + 32 +.....+ 102).
Sumathi said:
1 decade ago
How do we get the value of {n(n+1)(2n+1)}/6?
Can please anyone tell me?
Can please anyone tell me?
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