All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Let be the statement:

When

is true.

Assume that is true for some , i.e.

Want to prove that is true, i.e.

LHS

Since is true and is true, hence by Mathematical Induction, is true for all

(ii)

(a)

…

(b)

As

Hence, is a convergent series, and the value of the sum to infinity is

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