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Algebra

Cool goIITian

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15 Mar 2008 14:13:41 IST

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618

sequences and series

None

_n=1

⁹⁹ n! ( n² + n +1 ) is equal to ?

ans: 100*(100!) -1

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Comments (13)

sandeep ramesh

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15 Mar 2008 14:17:34 IST

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telesopic sum only

make it n!(n+1)^2 - n!*n = (n+1)! * (n+1) - n!n = 100 * 100! - 1

Hari Shankar

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15 Mar 2008 14:17:36 IST

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Hint: write n²+n as n(n+1).

Mistimed

sandeep ramesh

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15 Mar 2008 14:18:25 IST

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but sir you dont get a telescopic sum

Hari Shankar

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15 Mar 2008 14:22:43 IST

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Sorry I had in mind sth like

n.n!

sharmadon

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15 Mar 2008 14:23:27 IST

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sandeepramesh cudnt understand the final step..pls explain in detail..

sandeep ramesh

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15 Mar 2008 14:25:33 IST

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the final step is the telescopic sum step n all the terms of (n+1)(n+1)! and n!n get cancelled except the first term of n!n and last term of (n+1)!(n+1)

If you cant understand nemore ask hsbhatt sir who's an excellent teacher n an expert

sharmadon

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15 Mar 2008 14:27:10 IST

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fine fine...was unable to understand the term telescopic sum..

Somye---- elegance personified

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15 Mar 2008 15:31:17 IST

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this can be done in this way

n! (n²+n+1)

=n! ((n+1)²-n)

now keep on substituting values till 1 to 99

ie n=1---- 2*2! - 1*1!

n=2 + 3*3!- 2*2!

n=3 + 4*4!-3*3!

+ ............... and so on

n=98 + 99*99! - 98*98!

n=99 + 100*100!- 99*99!

all terms are cancelled except 100*100! - 1

Somye---- elegance personified

Hot goIITian

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15 Mar 2008 15:34:58 IST

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plz rate IF USEFUL

sandeep ramesh

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15 Mar 2008 15:35:49 IST

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Plz dont rate if useful, thats the new policy here :P

Somye---- elegance personified

Hot goIITian

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15 Mar 2008 15:41:22 IST

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HaHaHa!!!!!!!!!!!!!!!!!!!!!

sandeep ramesh

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15 Mar 2008 15:53:12 IST

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Yes boo hoo Mr. Green

Somye---- elegance personified

Hot goIITian

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15 Mar 2008 16:13:49 IST

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HEY!! these pics of urs are great..r u owez like this ..keep this spirit goin

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