Question

Assertion :$(1.1{)}^{10000}>1000$ Reason: Using binomial theorem we can approximate $(1+x{)}^n=1+nx$ if $0<x<1$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$(1.1{)}^{10000}$

$=(1+0.1{)}^{10000}$

${=}^{10000}{C}_0{1}^{10000}{+}^{10000}{C}_1{1}^{9999}(0.1{)}^1+.......$

$=1+1000\cdot 0.1+..........$

$=1001+.......\therefore (1.1{)}^{10000}>1000also(1+x{)}^n{=}^n{C}_0{+}^n{C}_{1}x+.........=1+nx+....=1+nx$