Find the greatest value of n so that 1+5+52 +53+......to n terms is less than 4321.
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Asked on May 01, 2020 by
Keyz Vishvkarma
Number of natural numbers not exceeding 4321 can be formed with the digits 1,2,3,4 if repetition is allowed
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ANSWER
Case 1: Four- digit number
Total number of ways in which the 4 digit number can be formed =4×4×4×4=256
Now, the number of ways in which the 4− digit numbers greater than 4321 can be formed is a s follows :
Suppose, the thousand's digit is 4 and hundred's digit is either 3 or 4.
∴ Number of ways =2×4×4=32
But 4311,4312,43413,4314,4321 are less than or equal to 4321
∴ Remaining number of ways =256−(32−5)=229
Case 2: Three- digit number
The hundred's digit can be filled in 4 ways.
Similarly, the ten's digit and the units digit can also be filled in 4 ways each.
This is because the repetition of digits is allowed.
∴ Total number of three- digit number =4×4×4=64
Case 3: Two- digit number
The ten's digit an the unit's digit can be filled in 4 ways each. This is because the repetition of digits is allowed.
∴ Total number of two digits numbers =4×4=16
Case 4: One- digit number
Single digit number can only be 4
∴ Required numbers =229+64+16+4=313
Answer:
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