Find the sum to n terms of 0.8+0.88+0.888+....
Answers
sum to n terms of 0.8+0.88+0.888+.... = (8/81)(9n + 1/10ⁿ - 1)
Step-by-step explanation:
0.8+0.88+0.888+....
=8(0.1 + 0.11 +0.111 +...............................)
= 8(1/10 + 11/100 + 111/1000 +............................)
= (8/9)(9/10 + 99/100 + 999/1000 +..............................)
=(8/9) ((1 - 1/10) + (1 - 1/100) + (1 -1/1000) +.....................(1 - 1/10ⁿ)
= (8/9)(n - (1/10¹ + 1/10² + 1/10³ +..........................+ 1/10ⁿ))
GP a = 1/10 r = 1/10 n = n
sum = a(1 - rⁿ)/(1 - r) = (1/10) (1 - (1/10)ⁿ)/(1 - 1/0) = (1/10) (1 - (1/10)ⁿ)/(9/10)
= (1 - (1/10)ⁿ)/9
= (8/9) (n - (1 - (1/10)ⁿ)/9)
= (8/81)(9n + 1/10ⁿ - 1)
sum to n terms of 0.8+0.88+0.888+.... = (8/81)(9n + 1/10ⁿ - 1)
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