Calculus BC: Series

Problem : Does the series 1 + (- 1) + 1 + (- 1) + ^... converge?

Problem : Show that 1/n ² converges by grouping terms 2 and 3 , 4 through 7 , 8 through 15 , and so on using the fact that 1/2ⁿ converges.

Solution for Problem 2 >>

Note that

+	<	+
+ ... +	<	4
+ ... +	<	8

and so on, so (naively) the series is "less than" the series

1 + 2 +4 +8 + ... = 1 + + + + ...

which converges.

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