Question
Download Solution PDFएक समान्तर श्रेणी का प्रथम पद α है एवं प्रथम m पदों का योग शून्य है, तब अगले n पदों का योग होगा :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त संकल्पना:
समान्तर श्रेणी के प्रथम n पदों का योग
Sn = n/2[2a + (n - 1)d]
गणना:
प्रथम पद = a
Sm = 0
∴ m/2[2a + (m - 1)d] = 0
d = -2a/(m - 1) ---(i)
am + 1 = a + md
और अगले n पदों के लिए md पहला पद होगा।
Sn = n/2[2a + (n - 1)d]
Sn = n/2[2(a + md) + (n - 1)d]
⇒ n/2[2a + 2md + (n - 1)d]
⇒ n/2[2a + (2m + n - 1)d]
(i) से d रखें,
⇒ n/2[2a + (2m + n - 1)(-2a/(m - 1))]
n/2 × 2a [1 - (2m + n - 1)/(m - 1)]
⇒ an[(m - 1 - 2m - n + 1)/(m - 1)]
∴ Sm = an(n + m)/(1 - m)
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