How many terms of the series 2+2√2+4+.....amount to (30+14√2)?
Answers
Step-by-step explanation:
2+2√2+4+4√2+8+8√2+16 = 30 + 14√2
There are 7 terms of the series to get value of 30 + 14√2 .
Answer:
Step-by-step explanation:
Given,
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•a=2 r=√2 Sn= (30+14√2)
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•Sn= a(r^n-1)
-----------
r - 1
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• a(r^n-1)
------------- =(30+14√2)
r - 1
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• 2(√2^n-1)
---------------- = (30+14√2)
√2 -1
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• √2^n -1 (30+14√2)
------------ = -----------------× 1/2
√2- 1
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• √2^n -1 = 2(15+7√2)
----------- ----------------× 1/2
√2- 1
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• √2^n-1 = (15+7√2)
------------
√2- 1
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• √2^n- 1 =(15+7√2) × (√2- 1)
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• √2^n- 1 = 15(√2 )- 15(1) + 7√2(√2) -
7√2(1)
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• √2^n-1 = 15√2 - 15 + 14 - 7√2
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• √2^n-1 =15√2 - 7√2 - 15 + 14
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• √2^n-1 = 8√2 - 1
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• √2^n = 8√2 -1+1
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• √2^n =8√2
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• √2^ n = √2^7. (since √2^7=8√2)
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so, n=7