a series such as :-(adsbygoogle = window.adsbygoogle || []).push({});

∑ from n = 1 ,until m for n

can be found with the law of the sum of arithmetical series:-

[m(2a+(m-1)d)]/2

where :-

m= the number of terms

a= the first term in the series

d= the basic arithmetical

in the pervious example :-

a=1 , d=1 , m=m

when we solve the last information in the law we find :-

∑ from n = 1 ,until m for n = m(m+1)/2

for example :-

1+2+3+4+..........+18+19+20 = 20(20+1)/2 = 210

my question is :-

what about the series :-

∑ from n = 1 ,until m for n^2 ???

it isn't an artithmetical or even a geometrical series then :-

what kind of series is it ?

and how could they find that :-

∑ from n = 1 ,until m for n^2 = [m(m+1)(2m+1)]/6 ???

for example :-

(1^2)+(2^2)+(3^2)+(4^2)+(5^2)= 5(5+1)(2*5+1)/6 = 55

and thank you

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# The sum of series

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