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# What is the value of A=1*2+2*3+...+9*10?

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Senior CR Moderator
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What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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29 Nov 2016, 02:59
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15% (low)

Question Stats:

82% (01:53) correct 18% (02:05) wrong based on 127 sessions

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What is the value of A?
$$A=1 \times 2+2 \times 3+...+9 \times 10$$

A. 198
B. 240
C. 330
D. 440
E. 572

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Re: What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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29 Nov 2016, 03:26
N*(N+1)*(N+2)/3

Put N=9

We get 9*10*11/3=30*11=330

Sent from my ONE A2003 using GMAT Club Forum mobile app
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Re: What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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29 Nov 2016, 09:56
nguyendinhtuong wrote:
What is the value of A?
$$A=1 \times 2+2 \times 3+...+9 \times 10$$

A. 198
B. 240
C. 330
D. 440
E. 572

No way to deny parmeshwarsharma 's is the best way to solve this question...

$$A = ( 1*2 ) + (2*3) + ( 3*4) + (4*5) + (5*6) + (6*7) + ( 7*8 ) + ( 8*9 ) + (9*10)$$

$$A = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 + 90$$

$$A = ( 2 + 6 + 12 + 20 + 30 ) + ( 42 + 56 + 72 + 90 )$$

$$A = 70 + 260$$

$$A = 330$$

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Re: What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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29 Nov 2016, 10:38
Abhishek009 wrote:
nguyendinhtuong wrote:
What is the value of A?
$$A=1 \times 2+2 \times 3+...+9 \times 10$$

A. 198
B. 240
C. 330
D. 440
E. 572

No way to deny parmeshwarsharma 's is the best way to solve this question...

$$A = ( 1*2 ) + (2*3) + ( 3*4) + (4*5) + (5*6) + (6*7) + ( 7*8 ) + ( 8*9 ) + (9*10)$$

$$A = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 + 90$$

$$A = ( 2 + 6 + 12 + 20 + 30 ) + ( 42 + 56 + 72 + 90 )$$

$$A = 70 + 260$$

$$A = 330$$

Hi i did it the way you did.
I mean i tried using the using digit concept but since it was zero i found the value instead.
What did parmeshwarsharma do there?

Did he use the concept of summation?
As in sum of n terms is n*n+1/2 or something.
You mind explaining it a bit

Regards
Stone Cold
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Re: What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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29 Nov 2016, 11:09
stonecold wrote:
Hi i did it the way you did.
I mean i tried using the using digit concept but since it was zero i found the value instead.
What did parmeshwarsharma do there?

Did he use the concept of summation?
As in sum of n terms is n*n+1/2 or something.
You mind explaining it a bit

Regards
Stone Cold

$$t_1 = 1^2 + 1$$
$$t_2 = 2^2 + 2$$
____________
$$t_n = n^2 + n$$

$$S_n = ( t_1 + t_2.......t_n ) + ( 1 + 2 ....n )$$

$$S_n = \frac{n ( n + 1 ) ( 2n + 1 )}{6} + \frac{n ( n +1)}{2}$$

Solve it you will get

$$S_n = \frac{n( n+1 )( n+2 )}{3}$$

I highly recommend not to go into such details , GMAT doesn't want you to recognize it, if you are not familiar with the same.. Try to solve the method I have used if you are not familiar with the concept...
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Thanks and Regards

Abhishek....

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Re: What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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29 Nov 2016, 11:58
Please Kudos+1 if you like the solution
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What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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29 Nov 2016, 17:28
Here is the solution for this one.

$$3k(k+1)=k(k+1)[(k+2)-(k-1)]=-(k-1)k(k+1)+k(k+1)(k+2)$$

We have $$3A=3\times 1 \times 2 + 3 \times 2 \times 3 +...+ 3 \times 9 \times 10$$

Hence
$$\begin{split} 3\times 1 \times 2 &= - 0\times 1 \times 2 + 1 \times 2 \times 3\\ 3\times 2 \times 3 &= - 1\times 2 \times 3 + 2 \times 3 \times 4\\ &...\\ 3\times 9 \times 10 &= - 8\times 9 \times 10 + 9 \times 10 \times 11\\ 3\times 1 \times 2 + 3 \times 2 \times 3 +...+ 3 \times 9 \times 10 &= - 0\times 1 \times 2 + 9 \times 10 \times 11 \\ 3A &= 9 \times 10 \times 11\\ A&= \frac{ 9 \times 10 \times 11}{3} \end{split}$$
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Re: What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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16 Mar 2017, 14:58
parmeshwarsharma wrote:
N*(N+1)*(N+2)/3

Put N=9

We get 9*10*11/3=30*11=330

Sent from my ONE A2003 using GMAT Club Forum mobile app

What exactly is this formula?
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Re: What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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16 Mar 2017, 21:13
1
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nguyendinhtuong wrote:
What is the value of A?
$$A=1 \times 2+2 \times 3+...+9 \times 10$$

A. 198
B. 240
C. 330
D. 440
E. 572

So the nth term is given by

$$T_n = n * (n + 1)$$

$$T_n = n^2 + n$$

So the first term is equivalent to 1^2 + 1
The second term is equivalent to 2^2 + 2
The third term is equivalent to 3^2 + 3
...

If we add the 9 terms, we get: $$1^2 + 1 + 2^2 + 2 + 3^2 + 3 + ... 9^2 + 9$$

Note that we know how to handle these two:
1 + 2 + 3 ... + 9
This is given by n(n+1)/2 = 9*(10)/2 = 45
and
1^2 + 2^2 + 3^2 + ... + 9^2
This is given by n(n+1)(2n+1)/6 = 9*10*19/6 = 285

Total sum = 45 + 285 = 330

What is the source of this question? I doubt it is a GMAT specific source.
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Re: What is the value of A=1*2+2*3+...+9*10?  [#permalink]

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17 Mar 2017, 00:21
we can say that ant term can be expressed as N(N+1) = N^2 +N

summing up from 1 to 10 we get N(N+1)(2N+1)/6 + N(N+1)/2 . Put n = 10, we get the sum as 330
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Re: What is the value of A=1*2+2*3+...+9*10? &nbs [#permalink] 17 Mar 2017, 00:21
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