For a real number x - x - denotes the integral part of x - The value of -1-2-1-2-1-100-1-2-1-100-1-2-99-100- isA- 49B- 50C- 48D- 51

The correct option is B 50∵ [x] denotes the integral part of x. Hence, after term [1/2 + 50/100], each term will be one. Hence the sum of given series will be ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Standard Formulae - 1

For a real nu...

Question

For a real number x, [x] denotes the integral part of x. The value of $[\frac{1}{2}] + [\frac{1}{2} + \frac{1}{100}] + [\frac{1}{2} + \frac{1}{100}] + . . . + [\frac{1}{2} + \frac{99}{100}]$ is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 50
$∵ [x]$ denotes the integral part of x. Hence, after term $[\frac{1}{2} + \frac{50}{100}]$ , each term will be one. Hence the sum of given series will be 50

Suggest Corrections

Similar questions

Q. For a real number

x [x]

denotes the integral part of

x

. The value of

[\frac{1}{2}] + [\frac{1}{2} + \frac{1}{100}] + [\frac{1}{2} + \frac{2}{100}] + . . . . . . [\frac{1}{2} + \frac{99}{100}]

The sum of the coefficients of all the integral powers of x in $(1 + 3 \sqrt{x})^{100}$ is

Q. For

x \in R

, let

[x]

denotes the greatest integer

\leq x

, then the value of

[- \frac{1}{3}] + [- \frac{1}{3} - \frac{2}{100}] + . . . + [- \frac{1}{3} - \frac{99}{100}]

Q. Let

f (n) = [\frac{1}{2} + \frac{n}{100}]

where [x] denotes the integral part of x. Then the value of

\sum_{n = 1}^{100} f (n)

is?

Q. Let

f (n) = [\frac{1}{2} + \frac{n}{100}]

where

[x]

denotes the integral part of

x

. Then the value of

\sum_{n = 1}^{100} f (n)

Join BYJU'S Learning Program

For a real number x, [x] denotes the integral part of x. The value of [12]+[12+1100]+[12+1100]+...+[12+99100] is

The correct option is B 50∵[x] denotes the integral part of x. Hence, after term [12+50100], each term will be one. Hence the sum of given series will be 50

For a real number x, [x] denotes the integral part of x. The value of $[\frac{1}{2}] + [\frac{1}{2} + \frac{1}{100}] + [\frac{1}{2} + \frac{1}{100}] + . . . + [\frac{1}{2} + \frac{99}{100}]$ is

The correct option is B 50
$∵ [x]$ denotes the integral part of x. Hence, after term $[\frac{1}{2} + \frac{50}{100}]$ , each term will be one. Hence the sum of given series will be 50