The sum 1+13+231+2+13+23+331+2+3+⋅⋅⋅+13+23+33+⋅⋅⋅+1531+2+3+⋅⋅⋅+15−12(1+2+3+⋅⋅⋅+15) is equal to :
A
620
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B
660
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C
1240
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D
1860
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Solution
The correct option is A620 Sum =15∑n=113+23+⋅⋅⋅+n31+2+⋅⋅⋅+n−1215×162 =15∑n=1(n(n+1)2)2n(n+1)2−60 =1215∑n=1n2+1215∑n=1n−60 =12×15×16×316+12×15×162−60 =620