Question
Download Solution PDFश्रृंखला का योग ज्ञात कीजिए : (20 + 22 + 24 +........+28) × 3
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
(20 + 22 + 24 +........+28) × 3
प्रयुक्त सूत्र:
यह एक ज्यामितीय प्रगति है।
a = पहला पद, r = उभय-निष्ठ अनुपात
ज्यामितीय प्रगति का योग = [a(rn - 1)/(r - 1)]
गणना:
a = 1
r = (22/20) = 4/1 = 4
⇒ श्रृंखला का योग = [1 × (45 - 1)/(4 - 1)] × 3
⇒ श्रृंखला का योग = [1 × (210 - 1)/(3)] × 3
⇒ श्रृंखला का योग = [1 × (1024 - 1)]
⇒ श्रृंखला का योग = [1 × (1023)]
⇒ श्रृंखला का योग = 1023
∴ श्रृंखला का योग 1023 है।
Alternate Method
(20 + 22 + 24 +........+28) × 3
⇒ (1 + 4 + 16 + 64 + 256) × 3
⇒ 341 × 3 = 1023
∴ श्रृंखला का योग 1023 है।
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