Find x where x=11/3+11/8+11/15+11/24+11/35+11/48+11/63+11/80+11/99
Answers
Given : x=11/3+11/8+11/15+11/24+11/35+11/48+ 11/63+11/80+11/99
To Find : Value of x
Solution:
11/3 + 11/8 + 11/15 + 11/24 + 11/35 + 11/48 + 11/63 + 11/80 + 11/99
Taking 11 common
= 11 ( 1/3 + 1/8 + 1/15 + 1/24 + 1/35 + 1/48 + 1/63 + 1/80 + 1/99)
multiplying and dividing by 2
= (11 /2 )( 2/3 + 2/8 + 2/15 + 2/24 + 2/35 + 2/48 +2/63 + 2/80 + 2/99)
rewriting terms like 3 = 1 * 3 , 8 = 2 * 4 and so on till 99 = 9 * 11
= (11 /2 )( 2/(1 * 3) + 2/(2 * 4) + 2/(3 * 5) + 2/(4 *6) + 2/(5 * 7) + 2/(6 *8) +2/(7 * 9) + 2/(8 * 10) + 2/(9 * 11))
rewriting terms 2 = 3 - 1 , 2 = 4 -2 and so on till 2 = 11 - 9
= (11 /2 )( (3 - 1)/(1 * 3) + (4-2)/(2 * 4) + (5-3)/(3 * 5) + (6-4)/(4 *6) + (7-5)/(5 * 7) + (8-6)/(6 *8) +(9-7)/(7 * 9) + (10-8)/(8 * 10) + (11-9)/(9 * 11))
Splitting numerator terms
= (11/2) ( 1 - 1/3 + 1/2 - 1/4 + 1/3 - 1/5 + 1/4 - 1/6 + 1/5 - 1/7 + 1/6 - 1/8 + 1/7 - 1/9 + 1/8 - 1/10 + 1/9 - 1/11)
cancelling similar terms with opposite sign
= (11/2) ( 1 + 1/2 -1/10 - 1/11)
=(11/2) ( 3/2 - 21/110)
= 33/4 - 21/20
= 8.25 - 1.05
= 7.2
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Find x where x=11/3+11/8+11/15+11/24+11/35+11/48+ 11/63+11/80+11/99
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