# partial sum and harmonic series problem

• Apr 10th 2007, 06:19 PM
rcmango
partial sum and harmonic series problem

a.) Use (4) to show that if Sn is the nth partial Sum of the harmonic series then Sn <= 1 + Ln n

b.) The harmonic series diverges, but it does so very slowly. Use part (a) to show tat the sum of the first term is less than 15 and the sum of the first billion terms is less 22.

i'm having alot of trouble with this one.
• Apr 11th 2007, 12:41 AM
earboth
Quote:

Originally Posted by rcmango

a.) Use (4) to show that if Sn is the nth partial Sum of the harmonic series then Sn <= 1 + Ln n

b.) The harmonic series diverges, but it does so very slowly. Use part (a) to show tat the sum of the first term is less than 15 and the sum of the first billion terms is less 22.

i'm having alot of trouble with this one.

Hello,

in a) you are refering to a problem(?) equation(?) #(4) which I couldn't find

to b)

Use the given inequality: Sn <= 1 + Ln(n) . Therefore:

S_(1,000,000,000) <= 1 + Ln(1,000,000,000) <= 1 + 20.723...

which is obviously smaller than 22.