Home/Calculus II/Sequences and series/Integral testSection 14.6Integral testIf fff is positive, continuous, and decreasing, and an=f(n)a_n=f(n)an=f(n), thenFormulavizCopy LaTeX∑n=N∞an\sum_{n=N}^{\infty}a_nn=N∑∞anView detail →andFormulaCopy LaTeX∫N∞f(x) dx\int_N^{\infty}f(x)\,dx∫N∞f(x)dxView detail →have the same behavior.Remainder bound:Copy LaTeX∫N+1∞f(x) dx≤RN≤∫N∞f(x) dx.\int_{N+1}^{\infty}f(x)\,dx \le R_N \le\int_N^{\infty}f(x)\,dx.∫N+1∞f(x)dx≤RN≤∫N∞f(x)dx.View detail →
Remainder bound:Copy LaTeX∫N+1∞f(x) dx≤RN≤∫N∞f(x) dx.\int_{N+1}^{\infty}f(x)\,dx \le R_N \le\int_N^{\infty}f(x)\,dx.∫N+1∞f(x)dx≤RN≤∫N∞f(x)dx.View detail →