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visits member for 2 years, 3 months
seen 6 hours ago

6h
comment Find the remainder when $2^{561}$ is divided by $561$ using simple congruence properties.
@rsadhvika, How about this?
7h
comment Solve the following integration
math.stackexchange.com/questions/425603/…
15h
comment If $n \in \mathbb{N} - \{1\}$, $ a \in \mathbb{Z}$, and $gcd(a,n)=1$, show there is $1 \leq i<n$ with $n|(a^i -1)$.
Use cut-the-knot.org/do_you_know/pigeon.shtml
15h
comment Sum of products of numbers in a list
$$2\sum ab=(\sum a)^2-(\sum a^2)$$
18h
comment Prove that for all integers a and b, a + b and a − b are either both odd or both even.
So, $a+b=a-b+$ even, right? So, $a+b,a-b$ will have the same parity
18h
comment Prove that for all integers a and b, a + b and a − b are either both odd or both even.
$a+b+(a-b)=2a$ which is even, $a+b-(a-b)=2b$
19h
comment Congruence modulo proof
$$5|(a-1), (a-1)|(a^2-1)\implies \cdots$$
1d
comment Inequalities with variables that are integers
$$ac-bd=a(c-d)+d(a-b)>0$$
1d
comment Solve for $\theta$: $a = b\tan\theta - \frac{c}{\cos\theta}$
@Kyle, How about this?
1d
comment Evaluating $\lim_{x \to 0} \frac{(1 + \sin x + \sin^2 x)^{1/x} - (1 + \sin x)^{1/x}}{x}$
@ParamanandSingh, I also calculated $$\lim_{x\to0}(1+\sin x)^{\frac1x}$$
1d
comment Logs and indices questions
@cjferes, Thanks. I doubt the accuracy of the first question.
1d
comment Find the value of $f(x)$ for $x = 2 + 2^{2/3} + 2^{1/3}$
@MohitSingh, Hope you understood the typo which has been rectified now
1d
comment Find the value of $f(x)$ for $x = 2 + 2^{2/3} + 2^{1/3}$
@MohitSingh, How about this?
2d
comment Prove ${2n \choose r+1}$ is maximum for $r=n$
math.stackexchange.com/questions/722952/…
2d
comment How I could solve the trignometric equation
math.stackexchange.com/questions/228182/… and math.stackexchange.com/questions/521102/…
Sep
14
comment Integrate $\int\frac{3x^2+1}{(x^2-1)^3}$
@k170, de facto Partial Fraction Decomposition(mathworld.wolfram.com/PartialFractionDecomposition.html), has terms like $$\frac\gamma{(x-1)}+\frac\delta{(x-1)^2}$$ etc., right?
Sep
14
comment Need explanation how we got right hand side of expression from the left hand side
Multiply the denominator & the numerator by $$\prod_{t=1}^{n-r}t=(n-r)!$$
Sep
14
comment What is the rule behind this derivative?
@TrevörAnneDenise, How about this?
Sep
14
comment Show that $\arctan a+\arctan(\frac{1}{a})=\frac{\pi}{2}$
Related : math.stackexchange.com/questions/610261/… and math.stackexchange.com/questions/483465/…
Sep
14
comment how to determine sum of series step by step?
@MickA, Sorry for the typo