Question
Download Solution PDF\(99\frac{11}{99}+99\frac{13}{99}+99\frac{15}{99}+\ldots+99\frac{67}{99}\\(1\over99\) విలువ కనుగొనండి?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఉపయోగించిన సూత్రం:
Sn = [n x (a + an) ] /2
an = a + (n-1)d
d = వ్యత్యాసం లేదా తేడా
a = ప్రారంభ పదం
a n = చివరి పదం
n = నిబంధనల సంఖ్య
S n = n నిబంధనల మొత్తం
పరిష్కారం:
శ్రేణిని ఇలా వ్రాయవచ్చు:
\(1\over99\) [99x99+11 + 99x99+13 + ... + 99x99+67]
= \(1\over99\) [9812 + 9814 + 9816+ ... + 9868]
ఇప్పుడు, మనకు లభించే శ్రేణి, 9812, 9814,...,9868.
a = 9812
an = 9868
d = 9814 - 9812 = 2
9868= 9812 + (n-1) x 2
n - 1 = 56/2 = 28
n = 29
Sn = 29 x (9812 + 9868) / 2 = (29 x 19680)/2 = 570720/2 = 285360
కాబట్టి, శ్రేణి = 285360/99 = 95120/33
Last updated on Jun 11, 2025
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