Question
योगफल $\sum_{ k =1}^{20}(1+2+3+\ldots+ k )$ है ..............
$=\frac{1}{6} \times 20 \times 21 \times 22=1540$
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$ A = \{ (x,\,y):y = \frac{1}{x},\,0 \ne x \in R\} $
$B = \{ (x,\,y):y = - x,\,\,x \in R\} $, तब
$A =\left\{( x , y ) \in R \times R \mid 2 x ^{2}+2 y ^{2}-2 x -2 y =1\right\},$
$B =\left\{( x , y ) \in R \times R \mid 4 x ^{2}+4 y ^{2}-16 y +7=0\right\}$ तथा
$C =\left\{( x , y ) \in R \times R \mid x ^{2}+ y ^{2}-4 x -2 y +5 \leq r ^{2}\right\}$ है। तो $| r |$ का निम्नतम मान, जिसके लिए $A \cup B \subseteq C$ है, बराबर है