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	Minimum of n where ∞ ∑ n=1 1 n >1000000

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

In[15]:=

∞

∑

n=1

1

n

Infinite sum

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☑ Step-by-step solution

∞

∑

n=1

1

n

diverges to ∞

Partial sum formula

k

∑

n=1

1

n



H

k

H_n is the nth harmonic number »

Partial sums

More terms

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

In[9]:=

∞

∑

n=1

1

n

Infinite sum

Show tests

p-Series Test | ▾

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∞

∑

n=1

1

n

diverges to ∞

Possible intermediate steps

Use the p-series test to determine the convergence of the series:

∞

∑

n

1

n

The convergence of a series of the form

∞

∑

k

C

p

k

, where C and p are constants and C is nonzero, can be determined by examining the quantity p using the following comparisons:

If p>1, the series converges.

If p≤1, the series diverges.

Identify the p-value in

∞

∑

n

1

n

:

p1

Since p≤1, the series

∞

∑

n

1

n

diverges:

Answer:
	The series is divergent by the p-series test.

Partial sum formula

k

∑

n=1

1

n



H

k

H_n is the nth harmonic number »

Partial sums

More terms

Show points