Question
Download Solution PDFनिम्नलिखित श्रेढ़ी के पहले 20 पदों का योग क्या है?
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ..........
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + .......... + 20
प्रयुक्त अवधारणा:
पहले n क्रमागत संख्या का योग n(n+1)/2 है।
पहले n क्रमागत संख्या के वर्ग का योग n(n + 1)(2n + 1)/6 है।
गणना:
प्रश्न के अनुसार, हमारे पास है:
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ..........20 पदों तक
nवाँ पद = n(n + 1)
योग = ∑ n (n + 1) = ∑ (n2 + n)
योग = ∑ n2 + ∑ n
योग =
योग =
योग =
n = 20 रखने पर, हमारे पास है
योग =
⇒ योग =
⇒ योग =
⇒ योग = 3080
∴ दी गई श्रेढ़ी के पहले 20 पदों का योग 3080 है।
Last updated on Jul 2, 2025
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