Latest Book Aptitude Question SOLUTION: Sum the series 3+18+57+132+255+...to n terms.

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(#M40011050) BOOK question Sum of series Keep an EYE

Sum the series 3+18+57+132+255+...to n terms.

Asked In Book Shipra (11 years ago)

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Dr.Dipin Singh  (11 years ago)

n*(n+1)*(n^2+n+1)/2

Sn=3+18+57+132+255+.......... +an..............(1)
Sn=-- 3+18+57+132+255+........+a(n-1) +an........(2)
subt. (2) from (1)
0= 3+15+39+75+....-an
an = 3(1+5+13+25+41+...)= 3*( Sigma ( n^2+(n-1)^2)= 2n^3+n
then
Sn = sigma (2n^3+n)
= n*(n+1)*(n^2+n+1)/2

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