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∑k=111(2+3k)
∑k=1112+∑k=1113k
∑k=1112=2+2+2+...........(11times)
=2×11=22
∑k=1113k=3+32+33+........311
This series is a G.P. with first term= a=3, common ratio =r=323=3
and number of terms =n
We know that sum of n terms of a G.P=a.rn−1r−1
∴∑k=1113k=S11=3*(3¹¹−1)/(13−1)=32(3¹¹−1)
⇒∑k=111(2+3k)=22+32(3¹¹−1)
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