"If 210 + 29.31 + 28 .32 +.....+ 2.39 + 310 = S - 211, then S is equal to :"

"Let S 1 = 2 10 + 2 9 .3 1 + 2 8 \n.3 2 +.....+ 2.3 9 + 3 10 ....(1)\n Also ${{3{S_1}} \\over 2}$ = 2 9 .3 1 + 2 8 \n.3 2 +.....+ 2.3 9 + 3 10 + ${{{3^{11}}} \\over 2}$ ......(2)\n Performing (1) - (2), we get\n $- {{{S_1}} \\over 2} = {2^{10}} - {{{3^{11}}} \\over 2}$\n $\\Rightarrow$ S 1 = 3 11 - 2 11 \n According to question,\n 3 11 - 2 11 = S - 2 11 \n $\\Rightarrow$ S = 3 11 "

Medium MCQ +4 / -1 PYQ · JEE Mains 2020

If 2¹⁰ + 2⁹.3¹ + 2⁸ .3² +.....+ 2.3⁹ + 3¹⁰ = S - 2¹¹, then S is equal to :

A ${{{3^{11}}} \over 2} + {2^{10}}$
B 311 — 212
C 2.311
D 311 Correct answer

Solution

Let S1 = 210 + 29.31 + 28 .32 +.....+ 2.39 + 310 ....(1) Also ${{3{S_1}} \over 2}$ = 29.31 + 28 .32 +.....+ 2.39 + 310 + ${{{3^{11}}} \over 2}$ ......(2) Performing (1) - (2), we get $- {{{S_1}} \over 2} = {2^{10}} - {{{3^{11}}} \over 2}$ $\Rightarrow$ S1 = 311 - 211 According to question, 311 - 211 = S - 211 $\Rightarrow$ S = 311

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Subject: Mathematics · Chapter: Sequences and Series · Topic: Arithmetic Progression

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If 210 + 29.31 + 28 .32 +.....+ 2.39 + 310 = S - 211, then S is equal to :

Solution

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If 2¹⁰ + 2⁹.3¹ + 2⁸ .3² +.....+ 2.3⁹ + 3¹⁰ = S - 2¹¹, then S is equal to :