Number System practice question for Railways, SSC. Review the correct answer and explanation, then continue with related practice below.
1 2 + 1 6 + 1 12 + 1 20 + 1 30 + …… + 1 [n(n+1)] = ? 1 2 + 1 6 + 1 12 + 1 20 + 1 30 + …… + 1 [n(n+1)] = ? Explanation 2 = 1 (1×2) 1 6 = 1 (2×3) 1 12 = 1 (3×4) 1 20 = 1 (4×5) Therefore, the general term is: 1 [r(r+1)] Now, 1 [r(r+1)] = 1 r − 1 (r+1) Therefore, 1 (1×2) = 1 − 1 2 1 (2×3) = 1 2 − 1 3 1 (3×4) = 1 3 − 1 4 1 (4×5) = 1 4 − 1 5 ... 1 [n(n+1)] = 1 n − 1 (n+1) Hence, S = (1 − 1 2) (1 2 − 1 3) (1 3 − 1 4) ... (1 n − 1 (n+1)) All the middle terms cancel: −1 2 + 1 2 = 0 −1 3 + 1 3 = 0 −1 4 + 1 4 = 0 Therefore, S = 1 − 1 (n+1) Taking LCM: S = [(n+1) − 1] (n+1) = n (n+1) Hindi: [r(r+1)] = 1 r − 1 (n+1) = n (n+1)
व्याख्या: Observe: 1
प्रत्येक पद को इस प्रकार लिख सकते हैं: 1
(r+1) अतः सभी बीच के पद कट जाते हैं और बचता है: 1 − 1
Answer and explanation are free to read — no sign-in required.उत्तर और व्याख्या पढ़ने के लिए साइन-इन आवश्यक नहीं है।
Correct Answerसही उत्तर
D. n/(n+1)
Explanationव्याख्या
Explanation is not available for this older question yet. / इस पुराने प्रश्न की व्याख्या अभी उपलब्ध नहीं है।
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