Question

Question No. 4
What are the last two digits of x, if x = (11^1+ 11^2 + 11^3 +
+ 11^55)?
55
00
04
45​

Answer 1

Given :- What are the last two digits of x, if x = (11^1+ 11^2 + 11^3 + 11⁴ + 11^55)?

55

00

04

45

Answer :-

→ x = (11^1+ 11^2 + 11^3 + 11⁴ + 11^55)

→ x = 11(1 + 11 + 11² + 11³ + 11⁴)

→ x = 11( 1 + 11 + 121 + 1331 + 14641)

→ x = 11 * 16105

→ x = 11 * 05 = 55 in last (A) (Ans.)

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Answer 2

Given :  x = (11^1+ 11^2 + 11^3 + + 11^55)  

To Find : last two digits

Solution:

x= ( 11¹  + 11² + 11³ + ______ +  11⁵⁵)

=> x = 11 ( 1 + 11  + 11²  + ______ +   11⁵⁴)

all the term inside the bracket will end  1

and there are 55 terms   inside bracket

Hence get 55

so unit digit inside bracket = 5

11 ( unit digit 5)

= 55  

Hence last two digits of x  = 55

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