But she finished. And the solution bank said “Correct.” Her heart beat a little faster. ib math aa hl exam questionbank

Prove by mathematical induction that for all n ∈ ℤ⁺, Σ_{k=1}^n (k * k!) = (n+1)! – 1. But she finished

She closed her eyes and dreamed of limits that didn't diverge. ” she whispered

“Okay,” she whispered, pulling out a fresh sheet of paper. “Integration by parts. Twice. Then a trick.” Her pen flew, sketching the cyclic dance of derivatives. sin(x) becomes cos(x) becomes -sin(x) . e^x stays e^x . She wrote the lines, the u and dv, the careful subtraction. Ten minutes later, she had an answer: (e^π + 1)/2 .