Why is it intuitively "obvious" that: $2^0+2^1+2^2+...+2^n=2^{n+1}-1$
78632
Summation equation for $2^{x-1}$
92046
Proving $\sum\limits_{i=0}^n  i 2^{i-1} = (n+1) 2^n - 1$ by induction
122006
Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
142132
How do you prove $\sum \frac {n}{2^n} = 2$?
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
96554
Why is $x^0 = 1$ except when $x = 0$?
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
69131
Different proofs of $\,a^n-b^n =(a-b)\sum_{i=0}^{n-1} a^i b^{n-1-i} $?
150320
Why does $a^{b}·a^{c}=a^{b+c}$?
24572
Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
71534
Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$
69943
why is ${n+1\choose k} = {n\choose k} + {n\choose k-1}$?
146200
proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
46144
Understanding imaginary exponents