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what is the sum of

51x52, 52x53, 53x54...100x101?

- 9Comments
- @webby it is in the form n(n+1) = n^2+n , no hit and tria.... 12 Oct.
- 51 * (51+1) + 52 * (52 + 1) ................ which is 51.... 12 Oct.

Max S
@Bing05
13

@webby summation of first 100 terms - summation of first 50 terms ( nth term = n^2+n)

vaibhav
@webby
34

@Bing05 could you tell me how you generally find the nth term of a series(any series)..do you follow any method or is it just hit and trial?

Max S
@Bing05
13

@webby it is in the form n(n+1) = n^2+n , no hit and trial......but u can verify with the few terms given , first sum up 100 terms using n(n+1)(2n+1)/6 and n(n+1)/2 and subtract it from summation of first 50 terms..generally series are in AP,GP,HP or AG or some differences in pattern upto 2 degree or more.

Rahul Doodi
@rahul.doodi1
13

51 * (51+1) + 52 * (52 + 1) ................

which is 51^2 + 52^2 +......... 100^2 + ( 51 + 52........+100)

Summation and get

how many 3 digit natural nos have less than 5 prime factors?

- 7Comments
- 900. 12 Oct.
- 999 -> 3^2*11^2 100 - > 5^2 * 2^2 999-101=900. 12 Oct.

how to find the unit digit of (1273)^122!?

- 12Comments
- 1. 08 Oct.
- . 09 Oct.

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