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If $S_1,S_2,S_3,\dots\dots,S_m$ are the sum of first $n$ terms of $m$ arithmetic progressions, whose first terms  are $1,4,9,16,\dots,m^{2}$ and common differences are $1,2,3,4,\dots m$ respectively, then the value of $S_1+S_2+S_3+\dots \dots +S_m$ is :

  1. $\dfrac{mn(m+1)}{2} \\$
  2. $\dfrac{mn(2m+1)}{3} \\$
  3. $\dfrac{mn[3(m+1)+1]}{6} \\$
  4. $\dfrac{mn(m+1)(4m+3n-1)}{12}$
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