Find out if ∑ k = 1 ∞ k + 1 2 k convergesI have split it into ∑ k = 1 ∞ k + 1 2 k = ∑ k = 1 ∞ k 2 k + ∑ k = 1 ∞ 1 2 k ,and applied the geometric series to the second part of the sum. But how do I deal with the first one to find the limit?

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Find out if       ∑          k      =      1              ∞                          k        +        1                    2        k             convergesI have split it into       ∑          k      =      1              ∞                          k        +        1                    2        k              =      ∑          k      =      1              ∞                  k              2        k              +      ∑          k      =      1              ∞                  1              2        k              ,and applied the geometric series to the second part of the sum. But how do I deal with the first one to find the limit?

Dillon Levy · Accepted Answer

Because for all   k  ≥  10 we have       2    k    &amp;gt;      k    3   and      ∑          k      =      10              +      ∞            1          k      2      converges.

Find out if sum_(k=1)^oo((k+1)/(2^k)) converges

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