Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

ICSE Class 10 Answered

Given 1/(1*2*3)+1/(2*3*4)+.....+1/(98*99*100)=a/b. Find (b-a).
Asked by arpitadas4117 | 17 Jan, 2022, 14:13: PM
answered-by-expert Expert Answer
fraction numerator 1 over denominator 1 cross times 2 cross times 3 end fraction plus fraction numerator 1 over denominator 2 cross times 3 cross times 4 end fraction plus... plus fraction numerator 1 over denominator 98 cross times 99 cross times 100 end fraction equals straight a over straight b straight T subscript straight n equals fraction numerator 1 over denominator straight n open parentheses straight n plus 1 close parentheses open parentheses straight n plus 2 close parentheses end fraction equals 1 half open square brackets fraction numerator 1 over denominator straight n open parentheses straight n plus 1 close parentheses end fraction minus fraction numerator 1 over denominator open parentheses straight n plus 1 close parentheses open parentheses straight n plus 2 close parentheses end fraction close square brackets straight T subscript 1 equals 1 half open square brackets fraction numerator 1 over denominator 1 cross times 2 end fraction minus fraction numerator 1 over denominator 2 cross times 3 end fraction close square brackets straight T subscript 2 equals 1 half open square brackets fraction numerator 1 over denominator 2 cross times 3 end fraction minus fraction numerator 1 over denominator 3 cross times 4 end fraction close square brackets straight T subscript 3 equals 1 half open square brackets fraction numerator 1 over denominator 3 cross times 4 end fraction minus fraction numerator 1 over denominator 4 cross times 5 end fraction close square brackets ... straight T subscript 98 equals 1 half open square brackets fraction numerator 1 over denominator 98 cross times 99 end fraction minus fraction numerator 1 over denominator 99 cross times 100 end fraction close square brackets fraction numerator 1 over denominator 1 cross times 2 cross times 3 end fraction plus fraction numerator 1 over denominator 2 cross times 3 cross times 4 end fraction plus... plus fraction numerator 1 over denominator 98 cross times 99 cross times 100 end fraction equals 1 half open square brackets fraction numerator 1 over denominator 1 cross times 2 end fraction minus fraction numerator 1 over denominator 99 cross times 100 end fraction close square brackets equals 1 half open square brackets fraction numerator 4950 minus 1 over denominator 9900 end fraction close square brackets equals 4949 over 19800 equals straight a over straight b Therefore comma space straight b minus straight a equals 14851
Answered by Renu Varma | 18 Jan, 2022, 13:26: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
ICSE 10 - Maths
sum of 10 tems of ap is 35 and sum of 9 terms of ap is 28. find the 10th term of an ap.
Asked by astonfern123 | 14 Jul, 2024, 20:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
Find the sum of first 24 terms of an A.P, whose nth term is given by an=3+2n
Asked by musarathh19 | 27 May, 2024, 19:45: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
the sum n terms of the series root2+root8+ root 18+root 32
Asked by srilakshmivytla28 | 10 Sep, 2023, 09:19: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
The 5th and 9th terms of an arithmetic progression are 4 and -12 respectively. Find (a) the first term (b) common difference (c) sum of 16 terms of the AP
Asked by varma.renu9481 | 13 Mar, 2023, 11:46: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
When do we use s=n/2(a+l) formula and when do we use s=n/2 x {2a+(n-1)d} formula in the sum of a.p?
Asked by rashikulkarni28 | 14 Aug, 2022, 16:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
In arithmetic progression , when we use s=n/2 [2a+(n-1)d] then why use a=(n-1)d formula?
Asked by rashikulkarni28 | 14 Aug, 2022, 16:30: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
Given 1/(1*2*3)+1/(2*3*4)+.....+1/(98*99*100)=a/b. Find (b-a).
Asked by arpitadas4117 | 17 Jan, 2022, 14:13: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
mrs gupta replace her total lone of 1,18000 by paying instalments every month. if the instalment for first month is 1000 and it increase by 100 every month ? what amount of lone she still has to pay after the 30 th instalment
Asked by preeti31122005 | 14 Aug, 2021, 13:08: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
the sum of first 6 terms of an A.P is 63 .The ratio of the 10th term to the 20th term is 1:2 . calculate the first and the 15th terms
Asked by savithakotari962 | 08 Feb, 2021, 20:40: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
ICSE 10 - Maths
  The algebraic expression of a sequence is 81-8n. What is 10th term What is the sum of 1st 10 terms whether the sum of any number of terms of the sequence will be 400? Why?
Asked by stehyeapen | 19 Oct, 2020, 13:11: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Are You a Teacher or a Parent Seeking Customised Tests? Click here
×