Mathematics, 19.09.2020 01:01 blessednish86orogbi

For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[infinity]Sn to obtain the value of the series or state that the series diverges. 1) ∑[infinity]k = 1(1/k + 1 - 1/k + 2).
2) ∑[infinity]k = 1(1/(k + 6)(k + 7).

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[infinity]Sn to obtain the value of the series or state that the series diverges. 1) ∑[infinity]k = 1(1/k + 1 - 1/k + 2). 2) ∑[infinity]k = 1(1/(k + 6)(k + 7).

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[infinity]Sn to obtain the value of the series or state that the series diverges. 1) ∑[infinity]k = 1(1/k + 1 - 1/k + 2).
2) ∑[infinity]k = 1(1/(k + 6)(k + 7).