Divergent condition of a series.












-2












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For $s>0$ when the following series will diverge $$sum_{k=1}bigg(frac{2^k}{1+2^k}bigg)^{2s}.$$






real-analysis sequences-and-series divergent-series







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    We would love to see your attempts too, try some manipulation of terms.
    $endgroup$
    – Akshar Gandhi
    Jan 15 at 14:45
















-2












$begingroup$


For $s>0$ when the following series will diverge $$sum_{k=1}bigg(frac{2^k}{1+2^k}bigg)^{2s}.$$






real-analysis sequences-and-series divergent-series







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    We would love to see your attempts too, try some manipulation of terms.
    $endgroup$
    – Akshar Gandhi
    Jan 15 at 14:45














-2












-2








-2





$begingroup$


For $s>0$ when the following series will diverge $$sum_{k=1}bigg(frac{2^k}{1+2^k}bigg)^{2s}.$$






real-analysis sequences-and-series divergent-series







share|cite|improve this question









$endgroup$




For $s>0$ when the following series will diverge $$sum_{k=1}bigg(frac{2^k}{1+2^k}bigg)^{2s}.$$






real-analysis sequences-and-series divergent-series




real-analysis sequences-and-series divergent-series






share|cite|improve this question













share|cite|improve this question











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asked Jan 15 at 14:36









MathRockMathRock

316




316








  • 1




    $begingroup$
    We would love to see your attempts too, try some manipulation of terms.
    $endgroup$
    – Akshar Gandhi
    Jan 15 at 14:45














  • 1




    $begingroup$
    We would love to see your attempts too, try some manipulation of terms.
    $endgroup$
    – Akshar Gandhi
    Jan 15 at 14:45








1




1




$begingroup$
We would love to see your attempts too, try some manipulation of terms.
$endgroup$
– Akshar Gandhi
Jan 15 at 14:45




$begingroup$
We would love to see your attempts too, try some manipulation of terms.
$endgroup$
– Akshar Gandhi
Jan 15 at 14:45










1 Answer
1






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1












$begingroup$

Hint: what happens to the summand as $k$ gets large?






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  • $begingroup$
    Can you say more??
    $endgroup$
    – MathRock
    Jan 15 at 14:41










  • $begingroup$
    Look up the divergence test.
    $endgroup$
    – Tom Himler
    Jan 15 at 15:22











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1 Answer
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1 Answer
1






active

oldest

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active

oldest

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active

oldest

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1












$begingroup$

Hint: what happens to the summand as $k$ gets large?






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Can you say more??
    $endgroup$
    – MathRock
    Jan 15 at 14:41










  • $begingroup$
    Look up the divergence test.
    $endgroup$
    – Tom Himler
    Jan 15 at 15:22
















1












$begingroup$

Hint: what happens to the summand as $k$ gets large?






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Can you say more??
    $endgroup$
    – MathRock
    Jan 15 at 14:41










  • $begingroup$
    Look up the divergence test.
    $endgroup$
    – Tom Himler
    Jan 15 at 15:22














1












1








1





$begingroup$

Hint: what happens to the summand as $k$ gets large?






share|cite|improve this answer









$endgroup$



Hint: what happens to the summand as $k$ gets large?







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 15 at 14:37









Robert IsraelRobert Israel

324k23214468




324k23214468












  • $begingroup$
    Can you say more??
    $endgroup$
    – MathRock
    Jan 15 at 14:41










  • $begingroup$
    Look up the divergence test.
    $endgroup$
    – Tom Himler
    Jan 15 at 15:22


















  • $begingroup$
    Can you say more??
    $endgroup$
    – MathRock
    Jan 15 at 14:41










  • $begingroup$
    Look up the divergence test.
    $endgroup$
    – Tom Himler
    Jan 15 at 15:22
















$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41




$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41












$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22




$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22


















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