Calculus Examples

$\sum_{i = 59}^{61} e^{i} + \ln (i)$

Step 1

Expand the series for each value of $i$ .

$e^{59} + \ln (59) + e^{60} + \ln (60) + e^{61} + \ln (61)$

Step 2

Simplify.

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Step 2.1

Replace $e$ with an approximation.

${2.71828182}^{59} + \ln (59) + e^{60} + \ln (60) + e^{61} + \ln (61)$

Step 2.2

Raise $2.71828182$ to the power of $59$ .

$42012104037900600000000000 + \ln (59) + e^{60} + \ln (60) + e^{61} + \ln (61)$

Step 2.3

Replace $e$ with an approximation.

$42012104037900600000000000 + \log_{2.71828182} (59) + e^{60} + \ln (60) + e^{61} + \ln (61)$

Step 2.4

Log base $2.71828182$ of $59$ is approximately $4.07753744$ .

$42012104037900600000000000 + 4.07753744 + e^{60} + \ln (60) + e^{61} + \ln (61)$

Step 2.5

Add $42012104037900600000000000$ and $4.07753744$ .

$42012104037900600000000004.078 + e^{60} + \ln (60) + e^{61} + \ln (61)$

Step 2.6

Replace $e$ with an approximation.

$42012104037900600000000004.078 + {2.71828182}^{60} + \ln (60) + e^{61} + \ln (61)$

Step 2.7

Raise $2.71828182$ to the power of $60$ .

$42012104037900600000000004.078 + 114200738981556000000000000 + \ln (60) + e^{61} + \ln (61)$

Step 2.8

Replace $e$ with an approximation.

$42012104037900600000000004.078 + 114200738981556000000000000 + \log_{2.71828182} (60) + e^{61} + \ln (61)$

Step 2.9

Log base $2.71828182$ of $60$ is approximately $4.09434456$ .

$42012104037900600000000004.078 + 114200738981556000000000000 + 4.09434456 + e^{61} + \ln (61)$

Step 2.10

Add $114200738981556000000000000$ and $4.09434456$ .

$42012104037900600000000004.078 + 114200738981556000000000004.09 + e^{61} + \ln (61)$

Step 2.11

Add $42012104037900600000000004.078$ and $114200738981556000000000004.09$ .

$156212843019456600000000008.17 + e^{61} + \ln (61)$

Step 2.12

Replace $e$ with an approximation.

$156212843019456600000000008.17 + {2.71828182}^{61} + \ln (61)$

Step 2.13

Raise $2.71828182$ to the power of $61$ .

$156212843019456600000000008.17 + 310429793570157000000000000 + \ln (61)$

Step 2.14

Replace $e$ with an approximation.

$156212843019456600000000008.17 + 310429793570157000000000000 + \log_{2.71828182} (61)$

Step 2.15

Log base $2.71828182$ of $61$ is approximately $4.11087386$ .

$156212843019456600000000008.17 + 310429793570157000000000000 + 4.11087386$

Step 2.16

Add $310429793570157000000000000$ and $4.11087386$ .

$156212843019456600000000008.17 + 310429793570157000000000004.11$

Step 2.17

Add $156212843019456600000000008.17$ and $310429793570157000000000004.11$ .

$466642636589613600000000012.28$