Live practice

Use the sequence definition or geometric-progression formula, keeping the first-term offset explicit.

The displayed substitutions cover every requested part and verify the result against the original data.

Proceed from the given expression and keep every transformation explicit.

The last line satisfies the required domain and establishes the result.

Reverse the pH definition: [H⁺]=10⁻ᴾᴴ.

Let the proton count be Z. Then N=1.317Z and A=N+Z=81.

Treat SSSS as one object. The remaining letters have repetitions A³, I² and N².

Let \(x\in B\). If \(x\in A\), then \(x\in A\cap B=A\cap C\), so \(x\in C\). If \(x\notin A\), then \(x\in A\cup B=A\cup C\); because \(x\notin A\), it must lie in \(C\). Thus \(B\subset C\).

Interchanging \(B\) and \(C\) gives \(C\subset B\). Therefore \(B=C\).

Apply the definition or the stated differentiation rules term by term.

Substitution into the original expression verifies the stated domain and final value.

Translate every condition into an equation and retain exact values throughout the ellipse calculation.

The last line satisfies the original conditions and supplies every requested part.

Translate every condition into an equation and retain exact values throughout the straight-line calculation.

The last line satisfies the original conditions and supplies every requested part.

Use the sequence definition or geometric-progression formula, keeping the first-term offset explicit.

The displayed substitutions cover every requested part and verify the result against the original data.