{"status": "success", "data": {"description_md": "If $n$ is a multiple of $4$, the sum $s = 1 + 2i + 3i^2 + \\ldots + (n+1)i^n$, where $i = \\sqrt{-1}$, equals:\n\n$\\text{(A)}\\ 1+i\\qquad\\text{(B)}\\ \\frac{1}{2}(n+2)\\qquad\\text{(C)}\\ \\frac{1}{2}(n+2-ni)\\qquad\\text{(D)}\\ \\frac{1}{2}[(n+1)(1-i)+2]\\qquad\\text{(E)}\\ \\frac{1}{8}(n^2+8-4ni)$\n\n___\n\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.\n", "description_html": "<p>If <span class=\"katex--inline\">n</span> is a multiple of <span class=\"katex--inline\">4</span>, the sum <span class=\"katex--inline\">s = 1 + 2i + 3i^2 + \\ldots + (n+1)i^n</span>, where <span class=\"katex--inline\">i = \\sqrt{-1}</span>, equals:</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 1+i\\qquad\\text{(B)}\\ \\frac{1}{2}(n+2)\\qquad\\text{(C)}\\ \\frac{1}{2}(n+2-ni)\\qquad\\text{(D)}\\ \\frac{1}{2}[(n+1)(1-i)+2]\\qquad\\text{(E)}\\ \\frac{1}{8}(n^2+8-4ni)</span></p>\n<hr>\n<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "1964 AHSME Problem 34", "can_next": true, "can_prev": true, "nxt": "/problem/64_ahsme_p35", "prev": "/problem/64_ahsme_p33"}}