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7h
awarded  Nice Answer
10h
comment Binomial coefficients in Geometric summation
@JaspreetSingh : the last step is just the binomial theorem: $$\sum_{k=0}^{N}\binom{N}{k}x^k = (x+1)^k.$$
11h
answered Binomial coefficients in Geometric summation
11h
revised Find the value of this series
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12h
revised Some trouble with the induction
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12h
answered Find the value of this series
12h
awarded  Enlightened
15h
comment Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
Personally, I do not dislike to use atom bombs to crack small nuts, but how do you deal with monotonicity, given only the asymptotics for $H_n$?
15h
revised Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
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15h
comment Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
@math110: oh, you're right, thanks, now fixing.
15h
comment About the sum of $\sum_{n=1}^{\infty} \frac 1 {n(n+1)}$
The $n$-th partial sum is equal to $1-\frac{1}{n+1}$. The series is the limit of its partial sums, so the series just equals one.
15h
comment Two prove two lines in a triangle are parallel
It would be a good thing to tell what you tried and maybe add a picture.
15h
revised Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
added 9 characters in body; edited tags
15h
awarded  Nice Answer
15h
revised Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
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15h
comment Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
@LuisFelipeVillavicencioLopez: you are adding two positive terms but also subtracting one, since the sum for $a_{n+1}$ starts with $\frac{1}{n+2}$.
15h
answered Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
15h
awarded  Announcer
16h
answered How do I evaluate this : $\int_{0}^{\infty} \ln \left( 1 + \frac{a^{2}}{x^{2}}\right)\ dx $ for $a > 0$?
16h
comment Recursive sequence of square roots of previous elements
@Malin: you're welcome. In any case, I have to say that Cesaro-Stoltz gives an easier way.