# 1.If y = x + x2/2 + x3/3 + x4/4+...show that x = y - y2/2! + y3/3! -y4/4!+...2.How many numbers lying between 10 and 1000 can be formed with the digits 3,4,5 and 7?

41 Points
10 years ago

hi....wr r u frm?I m yaswanth frm Andhra..

jitender lakhanpal
62 Points
10 years ago

HI SHWETA

1) here we will use the concept of series we get by Taylor''s theorom

y = -ln(1-x)       u can easily find the series of ln(1+x) in any class 12 book in limits topic

from here you can find the inverse of y which is x = 1 - e^(-y)

now apply the series with the help of series of e^x you will get the answer

2) in this question lets find some cases

a) two digit number

now it can be visualised as arranging 4 elements in 2 places with repitition

ity is 4 * 4

b) three digit number

similarly you will get 4*4*4

there is only one 4 digit number 1000 which is not the number we are finding out

just above 2 cases will be there you will get the answer

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Jitender