The value of displaystyle∑n=110 displaystyle∑m=110(m2+n2) equals

Question

The value of displaystyle∑n=110 displaystyle∑m=110(m2+n2) equals (A) 4235 (B) 5050 (C) 7700 (D) none of these

Tardigrade Admin · Accepted Answer

displaystyle∑n=110 displaystyle∑m=110(m2+n2) = displaystyle∑n=110[(12+n2)+(22+n2)+⋅s+(102+n2)] =10[(1)2+(2)2+ ldots+(10)2]+10[(1)2+(2)2+ ldots+(10)2] =(20 ⋅ 10 ⋅ 11 ⋅ 21/6) =7700

Q. The value of $n = 1 \sum 10 m = 1 \sum 10 (m^{2} + n^{2})$ equals

4235

5050

7700

none of these

$n = 1 \sum 10 m = 1 \sum 10 (m^{2} + n^{2})$
$= n = 1 \sum 10 [(1^{2} + n^{2}) + (2^{2} + n^{2}) + \dots + (1 0^{2} + n^{2})]$
$= 10 [(1)^{2} + (2)^{2} + \dots + (10)^{2}] + 10 [(1)^{2} + (2)^{2} + \dots + (10)^{2}]$
$= \frac{20 \cdot 10 \cdot 11 \cdot 21}{6}$
$= 7700$

Q. The value of n=1∑10​m=1∑10​(m2+n2) equals