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A partial sum adds the first n terms. A convergent series approaches a finite limit.
Your solution
Work out the values, then press Check.
Find the pattern, accumulate the terms and see what survives.
A partial sum adds the first n terms. A convergent series approaches a finite limit.
Work out the values, then press Check.
AP: Tₙ = a + (n − 1)d and Sₙ = n[2a + (n − 1)d]/2.
GP: Tₙ = arⁿ⁻¹. For r ≠ 1, Sₙ = a(1 − rⁿ)/(1 − r). If |r| is less than 1, S∞ = a/(1 − r). If r = 1, Sₙ = na.
Partial fractions: 1/[(k+p)(k+q)] = A/(k+p) + B/(k+q), where A = 1/(q−p) and B = −A. Adjacent terms may cancel when summed.