(i) (1\cdot2+3\cdot4+5\cdot8+7\cdot16+\cdots)
(t_n=(2n-1)\cdot 2^n)
[ S_n=\sum_{k=1}^{n}(2k-1)2^k ] Using standard AG sum method: (S=1\cdot2+3\cdot4+5\cdot8+\cdots+(2n-1)2^n)
11TH•Mathematics•Sequences And Series•Question 4
(i) \(1\cdot2+3\cdot4+5\cdot8+7\cdot16+\cdots\)
Sum to $n$ terms the following series:
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