1.

If (1/21) + (1/22) + (1/23) _______ (1/210) = 1/k, then what is the value of k?1). 512/5112). 1024/10233). 511/5124). 1023/1024

Answer»

(1/21) + (1/22) + (1/23) + ? + (1/210) = 1/k

⇒ 1/k = 1/2 × [1 – (1/210)] / (1 – 1/2) [? SUM of N terms in G.P. = a [(rn – 1) / (r – 1)]

⇒ 1/k = 1/2 × [1 – 1/1024] / (1/2)

⇒ 1/k = 1 – 1/1024

⇒ 1/k = 1023/1024

∴ k = 1024/1023


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