Question

plz solve this.... it's urgent​

Answer 1

Answer:

answer is d

Step-by-step explanation:

2/3

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Answer 2

Step-by-step explanation:

Given  to find the sum of infinite series 1/9 + 1/18 + 1/30 + 1/45 + 1/63 +-------------

• But 1/30 / 1/18 is not equal to 1/18 / 1/9  
• So this does not form a Geometric series.
• So 1/3 (1/3 + 1/6 + 1/10 + 1/15 + 1/21+.---------------)
• 3 can be written as ½ (2 x 3)
• 6 can be written as ½ (3 x 4)  
• 10 can be written as ½ (4 x 5)
• Now denominator can be written as ½ n(n + 1) where n >=2
• Therefore 1/3 x 2 ∑ n = 2 to infinity 1/n(n +1)
• So 2/3 ∑ n = 2 to infinity (1/n – 1/n + 1)
• Now 2/3 lim N to infinity ∑n = 2 to N (1/n -  1/n+ 1)
• = 2/3 lim N to infinity (1/2 – 1/3) + (1/3 – ¼) + (1/4 – 1/5) + ---------+(1/N – 1/N + 1)
• Now cancelling all same terms we get
• = 2/3 lim N to infinity (1/2 – 1/ N + 1)
• We know that lim n to infinity = 0 and lim n to infinity 1/n + 1 = 0)
• Therefore 2/3 (1/2 – 0)
•             = 2/3 x ½
•            = 1/3